This was one of the best weeks I’ve had on KA in a long time. I made it through the Random Variables unit test (the ninth unit in Statistics and Probability) AND got through the last exercise I had left to do in ALL of the Math: High School and College section of KA. 🥳 Heading into this week, I thought I had a chance of passing the Random Variables unit test but didn’t think it was likely. There were 21 questions on the test and I’d only managed to get 7 or 8 in a row before getting a question wrong. That continued to be the case up until Saturday when all of a sudden I cruised through all 21 questions without much trouble. 🤷🏻‍♂️ I was more than content simply finishing off the unit test and didn’t expect to get through the exercise, but I gave it a shot and it turned out to be super easy and I passed it without a sweat. So, all in all, it was one of the more productive weeks I’ve had on KA in a long time, and I’m more pumped than ever to finish this whole thing off! 💪🏼😤

Here are seven questions from the unit test:

Statistics and Probability – Unit 9 – Random Variables – Unit Test

Question 1

It took me a few minutes to think through this question before answering it. It’s not hard to figure out, but it took me a minute to think through the fact that the net gain would be $10,000*0.6 and then you’d subtract the $2,000 from the difference. It then took me a second to think through the fact that the SD wouldn’t affected by subtracting $2,000 from the difference and that, since the SD of the distribution was nicely given to you as 0.69, you just multiply that by the potential net gain. Boom. 🧨

Question 2

I was on the ninth question when I got this one wrong. 😞 I didn’t know what to do, but when I saw KA’s solution that shows you simply subtract the mean scores (ie. 41 – 41 = 0), it made sense in a weird way. The SD being normally distributed sort of makes sense to me but I still find it confusing. Even though I was bummed that I got this question wrong, it was helpful review for me of z-tables and z-scores both of which I was able to quickly remember and find easy to understand. FYI, here are the z-tables I used:

Question 3

I initially got this question wrong and then made the notes you see above afterwards. The math here really isn’t all that difficult, but I don’t understand why subtracting the means from each other and finding the SD of the new distribution shows you the probability of Bruno being faster than Ali where the distribution crosses 0. I think I understand what is going on and how to do the math, but I don’t understand why the math works this way. ☹️

Question 4

I was debating about whether or not I should add my rough notes from this question, which clearly I decided to do. You can see that there’s not too much math involved here. The hard part is just deciphering what the question is asking you to do. These questions are super annoying because if they just said, “hey, multiply each value in the set by their respective probabilities and sum up their products”, that’d be MUCH easier for me to understand than trying to understand the whole story about insurance. 😡 In any case, I was glad that I got this question correct because last week I got a very similar question to this one after spending ~30 mins trying to figure out what I was supposed to do and not being able to.

Question 5

You may not be able to make sense of my notes above, but I basically solved this question the same way KA did. ☺️ However, instead of putting all the outcomes in a single table like KA, I made tables (that are maybe hard to understand) for each outcome of winning, drawing, and losing. Then I just counted the number of ways each outcome could come to be, and multiplied that number over the total possible outcomes (21) by the payouts to figure out the solution. 

Question 6

By the time I got to this question, I had reviewed normal distributions enough that I had these types of questions memorized. After realizing what I needed to do, it took me about 2 minutes to sum up the means, find the SD of the new distribution, and then use the z-score formula to find the z-score and cross reference the z-score with the z-table to find the probability of T > 717. Even though it was easy, it was still very satisfying to be able to do it without any trouble.

Question 7

This was the last question on the test and I was 💩ing my pants when I was answering it. I knew I solved it properly because I had already solved at least 10 questions just like this one in the past two weeks, but I kept second guessing myself thinking I had done something wrong. Anyways, it turned out that I didn’t do anything wrong (because I’m a genius), and so I got the question correct and breathed a HUGE sigh of relief. 😮‍💨

Like I mentioned, after I got through the test, I saw that the next course I had to work on was College Statistics. There are 14 units in the course but only one that wasn’t 100% complete: Unit 5, Exploring Two Variable Quantitative Data. There was a new exercise added to the unit titled Predict with Transformed Data which, based on the name, I thought was going to be super tough. It turned out to be the opposite of that, however, and I just needed to do some simple log calculations. I got all four questions correct in a row in about 15 mins. 

Below are three questions from the exercise. You can see that in my notes from the first question, I did a quick log/exponent conversion check stating: 

• 2³ = 8
• log₂(8) = 3
• ∴ 2^log_2(8) = 8

Remembering this conversion made answering these questions super straightforward, so I’m not going to bother commenting on any of them:

College Statistics – Unit 5 ­– Exercise 3 – Predict with Transformed Data

Question 8

Question 9

Question 10

And that was it for this past week! It was nice to end the week by crushing that exercise and easily remembering how to use log/exponent conversions to answer those questions. I now only have four unit tests left to do — 1 in College Statistics, and 3 in Multivariable Calculus. I’m assuming the unit tests in MC will be difficult, but they’ll be good review for me before I attempt the final thing I’ll need to do to finish this whole thing off which is the MC Course Challenge. It says I last attempted the Course Challenge a year ago and my score was 70%. I have a feeling it’s going to take me a few weeks to pass the Course Challenge with a score >90%, so it could be a few months before I wrap this whole thing up, but the finish line is getting SOOO close! I’m PUMPED to be just about done (…329 weeks later…), so hopefully I can capitalize on this momentum/motivation and finish off the Exploring Two Variable Quantitative Data unit test this coming week. There are only 13 questions in it so, depending on how hard the questions are, I definitely think it’s possible!

As always, fingers crossed! 🤞🏼