I’ve had worse weeks on KA, but this one certainly wasn’t my best. I was working on the Random Variables unit test but did pretty poorly on it. There are 21 questions on the test and the most questions I got through before getting one wrong was seven. That said, there were a number of questions that I found pretty straightforward and simple to think through, and some questions where I wasn’t completely sure what I was doing but was able to remember and reason my way to the solution, so I at least had that going for me which was nice. But on the other hand, there were also quite a few questions that came up against where I was completely lost and didn’t have a clue what I needed to do to solve them. On those questions, the math wasn’t actually that difficult, they just had concepts in them that I completely forgot about and didn’t know what to do. The silver lining is that I likely spent 6–7 hours working on KA which hasn’t generally been the case over the past few months. I’m pretty fired up right now to get through KA given how close I am to finishing everything off, so even though I got rocked this week, I’m feeling pretty good that I’ll be able to not only get through this unit test soon but also finish off all of the KA’s Math section soon, as well! 💪🏼

Here are eight questions from the unit test:

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

Question 1

I got this question wrong but knew the correct way to solve it, I just made a stupid error. 😡 When I calculated the expected value, I multiplied (0.9)⁶(50) = 26.57205 which I then rounded to 27 and (1 – (0.9)⁶)(–50) = –23.42795 which I then rounded the answer to –23. My final answer was 27 – 23 = 4 which, as you can see from KA’s solution, was wrong…

Question 2

I didn’t really know what I was supposed to do on this question but was able to figure out that I needed to multiply the values in the left column by the values in the right column and add up their sums which summed up to 4,000 candy bars. Since there were 2,000 kids in the study, it was obvious that on average each kid sold 2 candy bars. 🧨

Question 3

I screwed this question up in multiple ways. First I thought I needed to find the probably of her winning exactly one time, not 0 times, as well. Second, I also forgot that you need to multiply the number of ways she could win by five since she could WLLLL, LWLLL, LLWLL, LLLWL, and LLLLW. This still doesn’t make complete intuitive sense to me, but I get general idea of what’s going on. I watched a video shown in the last screenshot above and sort of was able to remember how/why the combination function works and is what is needed here — but I’m still not completely sure.

Question 4

I have no idea how I solved this. I wasn’t planning on showing my rough notes but don’t know what else to do to try and explain how I figured it out. On my written note above, (1) is where I realized how many total rolls there were which was 150 + x + y (I crossed out the x and y and put in 75 after I figured it out). (2) was me multiplying each number of rolls by 20/500 to get the expected number of rolls for each number on 20 rolls, and then I multiplied the left column by the right column to get the product of the frequency by the value/number on the die, and then finding the sum of all the products. This totalled 46.4 which meant that 46.4 + 1x + 6y = 67.4, meaning x + 6y = 21. (3) was me doing some linear algebra to figure out that y = 75, and after that it was easy to figure out that x = 75 as well. 😮‍💨 

Question 5

I got smoked here. I don’t really know how to explain why I did it wrong, but suffice it to say I knew I had to find the sum of both distributions but for some reason, I tried to figure out the probability of one of distributions being at the given level and got it wrong. (That makes ZERO sense but I honestly don’t know how to explain why I screwed up this question.) BUT, the good thing is that after I got this question wrong and looked at KA’s answer, I realized these types of questions aren’t that hard. All you have to do is sum up the distributions and their SD’s, then figure out the probability at the given point in question of using a z-table and its z-score.

(What I just wrote could be completely wrong.)

Question 6

(INSERT SCREENSHOT)

I surprisingly got this question correct. I don’t have the energy to explain how it works, so hopefully my notes above can do the talking well enough for me.

Question 7

Again, didn’t really know what I was doing on this question but then it turned out that I did the math EXACTLY the right way. I don’t remember how/why the formulas for combinations or permutations work, but at least I did it properly. 🤷🏻‍♂️

Question 8

I was so annoyed getting this question wrong. I did way more math than I needed to because I didn’t understand what the question was asking. I thought I needed to subtract how much he saved from his insurance from the medical costs. Not sure if you can understand what I’m talking about or see it in my notes, but the bottom line was I only needed to calculate the probability of how much the insurance would cost and not figure out how much he would save given the probability of each type of medical cost. 😠

And that was it for this week. This wasn’t my best post in terms of clarity. I don’t think a lot of my explanations made too much sense. I need to review a lot of these concepts and then hopefully I’ll 1) get further along in the unit test, and 2) be able to speak about these concepts with a bit more clarity. In any case, I’ll say one more time that I’m SO excited get through KA and to be so close at this point! I’m optimistic that I’ll get through this unit test soon, maybe even by the end of the week. I think if I spent 8+ hours working on it this week, that would likely be more than enough. So, hopefully I can manage that and be on to the next unit test by Week… 330. 😳

As always, fingers crossed! 🤞🏼