~yeah i didn’t explain myself too well here, so:
Is how I’m answer all those questions.
the conditions are based off this:
I got this question
wrong because I had thought that since there was 0.5 it deal with probabilities. Even if it was a negative number. So I just answered it does not satisfy the first condition, since there was a negative output. The correct answer was that it does not satisfy the first condition and the second condition.
Oh they want you to mark every condition it violates? And you put 1 but they claim the answer is 1&2?
Logically I think 1&2 doesn’t make sense. If the -0.5 is a probability, then it violates 1 but not 2. If it’s not a probability, then it violates 2 but not 1. Claiming it violates both at once seems to involve claiming it both is and isn’t a probability. Depending on whether it’s a probability or not, 3 could also be violated.
I would have answered that 1 is violated. But more generally, I think it makes more sense to just figure out whether it works or doesn’t work. Trying to decide in which way(s) it doesn’t work can depend on interpretations.
Out of curiosity I looked at the professor’s lecture slides on that section and it shared this:
a) is the same as rule 1.) shared with me
b) should be the same as rule 3.)
It looks like the rule 2 about the function being defined as a probability function is not here. i think that makes sense and I think it resolves the issue you brought up.
been busy with work the past week and just spent free time doing classwork/homework.
11.6 Determinants and Cramer’s Rule:
Every square matrix has a number associated with it called its determinant.
The determinant of a 2 x 2 matrix is
To find the determinant of a matrix larger than 2 x 2 we need to use the minor and cofactor of a matrix entry.
The minor, M, of an entry, a, is the determinant of the matrix formed by deleting an i’th row and j’th column of A.
a.)M_11
Hmm. How do we know what the entry is? What are we finding the minor of? The 4 x 4 matrix formed by getting rid of the first row and first column is
so ad - bc = -30 - (-21) = -9.
b.)M_23 =
ad - bc = 24 - 0 = 24
So its the just the minor multiplied by either 1 or -1. So the cofactors and minor can be the same or opposite.
a) A_11 = -9 x -1^(1+1) = -9 x 1 = -9
b)A_23 = 24 x -1^(2+3) = 24 x -1 = -34
It can be shown that we can determine |A| by choosing any row or column, multiplying
each element in that row or column by its cofactor, and adding the results. This is called
expanding across a row or down a column.
Ok that’s enough to do the homework:
I got the second one wrong, I didn’t understand the rule fully/know how to use it correctly yet. I did find each of the cofactors. That was correct, but each of the cofactors have to be multiplied by original element and then added together. I just added the cofactors together. The correct answer was 30, not -7.
That’s not a 4x4 matrix.
Regarding both quotes:
When you don’t already know how to do something correctly with a low error rate, I think it’s important to slow down, take your time, and try to go step by step in an organized way. Focus on correctness before speed.
Being able to take some instructions or list of rules that you don’t have experience with, and follow it one by one, when you aren’t rushed, is an important skill that comes up in philosophy and other parts of life.
Woops. Yeah. I meant 2 by 2.
I agree. Though I’d be lying if I said I do this consistently.
For the issue that I posted about: I do remember doing that in a time crunch. I would say I started off this unit(?) strong and I had time to post as I go. Near the end of this unit (which is when I posted that) I was just trying to get homework assignments done so I could take the quiz and exam. The way it works is: complete a certain number of homework assignments, upon completion you get mastery points, get enough points and then you’re allowed to take the quiz and exam.
Though I probably would still rush at times if I felt confident even if I wasn’t in a time crunch. So that’s not good.
Anyways took the exam for this unit and got 100. So that’s neat I guess. Do I think I understand the math well? nah.
also: honorlock (a proctoring service) sucks so much. the most recent issue I had today was not knowing my macbook mic didn’t work with the screen closed. i have my macbook hooked up to a monitor and I just close it. apparently this affects the mic. that makes sense but i didn’t know that.
i took an exam before with the exact same set-up and i had no issues. this time it noticed on their system that the mic wasn’t on apparently. just confusing how it dinged this time and the other time it didn’t. exact same set-up and everything. just odd.
also before realizing how my closed macbook was the issue (in the end I just opened my macbook air and disconnected from the external display) they just nonchalantly were like “sorry none of our troubleshooting is working, i think you’ll have to fully restart honorlock, this may autosubmit your test and mess up your score” well thats nice. luckily i got it all worked out but it was still annoying,
From Chapter 5.4 Probability:
A number from 0 to 1 that represents the likelihood of an event occurring is referred to
as the event’s probability. A probability of 0 means that the event is certain not to occur,
and a probability of 1 means that the event is certain to occur. In this section, we will
see that integration is a useful tool for calculating some probabilities.
So this is an earlier chapter than the chapter I took notes on from before. Let’s see: I took notes on chapter 10.3 Discrete Probability Distributions. Weird that I’m now going back and taking notes/doing stuff on what sounds like the basics of probability.
I know this is a calculus text but so far I’ve avoided having to do any integration. I wonder if that trend will continue.
There are two types of probability, experimental and theoretical.
Experimental - based on actual events, you flip a coin a bunch of times, you get tails 52 out of 100 times, you then say the probability is 52/100
Theoretical - based on thinking/reasoning, you reason that since the two sides of a coin seem the same when you flip it it should have a 50% chance of lending on either side.
Suppose that we throw a dart at a number line in such a way that it always lands in the
interval [3, 5]. Let x be the number where the dart lands. There is an infinite number
of possibilities for x. Note that x can be observed (or measured) repeatedly and its
possible values comprise an interval of real numbers. Such a variable is an example of
a continuous random variable.
Continuous Random Variable -
its continuous, since their is no break in the values it can hold between 3 and 5. it can hold any and all values between their. the values just continue(?) from one point to another
its random, since it can take on any value in an interval
its variable, well x is defined here as the variable that takes on the differing values as we throw the dart at the number line
So previously I did probability mass functions. Now I’m doing density functions. Ok.
ok so we may be able to take the area of a subinterval which will give us the probability of x occurring in that sub-interval. ok.
i’m a bit confused on how it explained it, but looking at the picture of the graph it makes sense i think:
So the function here is y/f(x) = 1/3 ? And I guess since probability is defined to be from 0 to 1. You divide that 1 into three parts or something.
that makes sense from 3 to 4 it would be 33%
Looking at the next steps seems like this will involve integration. I’m going to try and integrate this:
ok so it looks like i got the integration part right, but i did the wrong thing it seems. doing the integral from 2 to 5 gave me 1.
1.) all outputs are positive
2.) the values all add up to 1
3.) that really doesn’t seem like a definition
Some homework:
Hmm. I’m only going to share one problem here because all of the problems for this homework were of the same kind.
It’s hard to prevent cheating when people take tests remotely, so the companies are rather intrusive, so students dislike them. I think that kind of difficult relationship with users, plus the difficulty of working with schools, doesn’t attract good businesses.
This comes up with chess too. Even with screen sharing, anti-cheat software running, and two webcams (normal cam and another behind the player showing their computer setup), cheating concerns and accusations continue. In person chess tournaments are still a lot more prestigious in part because they have a lot less cheating.
Was there a deadline and you got behind schedule? Or did you just decide to rush at some point?
What do you mean?
5.5 Probability: Expected Value; the Normal Distribution
Let’s again consider a dart thrown at a number line so that it lands somewhere in the
interval [3, 5]. We assume a uniform distribution, meaning that it is equally likely that
the dart will land on any one point in the interval.
Ok. I think this is different from what we assumed/did before.
Ok. So for the first part I understand that. You get a bunch of different values and then you get an average value for them. The second part and third I’m a little confused on. Let’s see:
The second part is just writing a formula for averages I think. Hmm. How do summation things work again? the bottom “i=1” is where we start summing from. The top n is the number we sum up to. Hmm. I think where I’m confused on is what the x_i represents. like just going off that formula. lets say n=2. how do we get different values of x?
For the third part. I remember summation formulas and integrals having some relationship but I never understood well how they work.
let’s see we have the integral from 3 to 5 x * f(x) x represents the terms and f(x) represents the number of terms you’re dividing by?
E(x) represents the expected value of the continuous random variable x. Ok. Just cause its random doesn’t mean there’s not a value it will usually take on.
So you can function for the random variable. Ok.
Also later on it says that the E(x) value is the same as the mean value.
so x is the continuous random variable again. ok.
So variance is equal to E(x^2)/the random variable being squared minus a squared mean.
Ok time for the homework:
So their having me use a table. Ok.
It would be the probability of 2.18 + 0.32
from the table: .4854 + .0910 = .5764
hmm i got it wrong. why? i looked at an example:
it looks like i had the right idea.
ahh i see. i looked at the table wrong.
the values are .4854 + .1255
P(1.68) - P(1.17) = .4535 - .3790 = 0.0745
Hmm I assume it would be the last value on the table (representing the end? of the standard normal distribution) minus P(2.37)
So: P(3.09) - P(2.37) = .4990 - .4911 = .0079
hmm. wrong. from the example
So .5 - .4911 = .0089
Hmm. So this time we’re given a mean and a standard deviation. Ok. I don’t even know how to start approaching this. So I’m just going to look at an example.
Ok. So I plugged the numbers in and got .25 <= z <= 1.5 (is there a better way to represent equal to?). I then apparently check that on a standard distribution table.
So: P(1.5) - P(0.5) = .4332 - 0.987 = .3345
There was a deadline and I got behind schedule. Well. Kinda.
This is a faster paced class for the summer. I believe 6 weeks roughly. An exam every two weeks. The way I pace it out is more or less based on how many mastery points (pretty much completing homework assignments with a 80%) I need to take the exam. To make it simple let’s say I had 28 mastery points to get. So I do 2 every day. However, things don’t work out that easily for me. Some day the home work is super easy, some days it takes a very long time. Sometimes the days I end up doing long homework are days I have a long work day. For this past section/exam I did end up behind schedule because one day I went to do the homework and it was quite tough after a long work day. So I skipped it for the day. That put me behind. Then my focus really went into just learning enough to get the home work done.
I mean my focus here isn’t too really learn this stuff well but I still want to try and understand what I can, but at that point I just wanted the minimum information to just do the homework.
Mmm. So it said “A function f is said to be a probability density function for x if:” and then it listed point 3 which says that:
Idk how to understand whats being said there as a definition of sorts (thats how i’m interpreting the if here). I understand thats something the probability density function can do, but I don’t understand why that plays a role into whether something is a probability density function.
You should build enough margin of error into your schedule. Scheduling 3 points per day and finishing early on day 10, leaving 4.66 days extra, would be reasonable.
And with 2 per day, you could do more than 2 on days when it’s easy to try to even out the work per day instead of evening out the number of points per day. Or you could schedule by hours instead of points.
They’re saying 3 has to be true. That has to actually work. If 3 is false, if a function can’t do that, then it isn’t a valid probability density function.
I think this is a major concern. You should know these concepts well to enable doing this kind of work.
The fuzzy memory on Sigmas isn’t great but you do seem to maybe know what they mean.
I’m concerned about subscripts. You shouldn’t be getting stuck on them if you want to understand the course topics which are advanced enough to be connecting with integrals. If you just want to pass the class then maybe you can do it anyway. I’m unclear exactly what’s going on but I’d recommend reviewing something even if you just want to pass. This may help: https://www.purplemath.com/modules/series.htm
Maybe you’re having trouble connecting symbols/math/algebra with words/meanings/data. The scenario is we throw a dart 100 times (or n times) and write down the data. The location it lands for throw 1 is named x1, the location for throw 2 is named x2, and the location for throw 100 is x100.
Or maybe you’re having issues with Sigmas. When you do a Sigma from i=1 (bottom) to 100 (top), you set i=1, then i=2, then i=3, etc. all the way up to 100 and add up all the results. So if you see xi then when i=1 that’ll be x1, when i=2 that’ll be x2, etc.
If one of my two explanations answered your question and the other didn’t, I’d like to know which one worked.
I skimmed through the post and I’ll read it more when I get back from work but one thing I wanted to share real quick:
Summation stuff, and I think you shared a link related to series and sequences?, are something I did bad in school in. So yeah this is an area I struggled with previously. Honestly I don’t think my memory is fuzzy on this. I think this is as well as I remember it in high school.
Fun(?) fact: my calculus 1 and 2 class were graded on a curve. The curve was set by setting the highest score on the exam to a 100. The teacher prided himself on the difficulty of the class. Scores varied on the subject but they varied from 12-40 (which were then curved to 100). I think the series test I took i got like a 12/100 or something.
In terms of passing the class I’m not too worried. Idk if I made it clear/shared this already, but the exams are just the homework questions with numbers changed around (same for the quiz). So long as I know how to get the answers for the homework questions I’m fine (which isn’t too big of an issue because almost every problem has explanations and step-by-step solutions on how to find the answer).
That being said I don’t enjoy not understanding and I find it frustrating to just learn how to purely get an answer for a question.
Ok. That makes sense. Oh. It didn’t keep your subscripts when I quoted. How do I fix that?
I think my confusion comes from when we start summing it. I haven’t looked at the resource you shared yet, but I get confused on how x takes on different values throughout the summation.
n is the term that will constantly change in my head. hmm. though i guess that wouldn’t make too much sense in the context i was given for this formula. you want to add up the values of all the x’s and then divide by n once. not keep adding them. hmm.
Oh. Ok. So in
n (the top part) is what we’re going up to and it happens to be used as a variable in the summation. however n doesn’t need to be part of the equation?
so if we got rid of 1/n from the above it would be summing the first term, the second term, the third term, etc. hmmm. that makes sense. i guess x_i would be defined elsewhere?
I think the second explanation addressed it.
I don’t know. Type the markup in by hand I guess. I used <sub>text</sub>
10.4: Continuous Probability Distributions: Mean, Variance, and Standard Deviation
Cumulative Density Functions:
“When we write a function in integral form and the variable (in this case, t) is a bound of the integral, we must use a different letter, called a dummy variable, for the variable in the integrand.” Hmm. Why? I guess this is probably due to not understanding integrals well?
Let’s say you have a function f(x) = x evaluated from [0,x]. What’s the issue with that. The integral of x is (x2 / 2) + C. Evaluated from 0 to x. What’s the issue? hmm.
Also what’s the point of doing this?
F(x) represents the cumulative density function
x is a value between [a,b], going up to, but not past, b.
1st point i understand. 2nd point i understand. third point, hmm
the probability is given by the second coordinate. like in (x,y) their referring to y? yes, because that is usually the coordinate representing the output. oh. hmm is this the value. this is equivalent of taking the integral of a to some number of the probability density function?
Got this wrong:
I’m confused how
probability of drawing a number card = 36/52
probability of drawing a spade card = 13/52
to find the probability of either drawing a number card or a spade card i do: P(number card) + P(spade card) - P(spade and number card)
the P(spade and number card) = 9/52, so
36/52 + 13/52 - 9/52 = 40/52
the odds are 40:12
they say the odds are 43:9, those seem like odds against getting a spade and number card.
nvm
they consider A a number card. is that normal? i don’t play many card games and stuff.
they’ve had similar questions where a little bit of background knowledge was involved
I was once given a question like
{Aquarius, Ares}
and told to describe this set
only one of the options was like {x| the set of astrology signs that start with s} i was like what if i knew nothing about astrology signs?
