Weekly Math Problem #67

Expectation & Variance. I am definitely aware that if you're not in, or will not be undertaking certain disciplines in college, there will be no need for you to take upper-level statistics courses. Most students I encounter only need entry level statistics courses to satisfy math credits and/or as prerequisite for a non-math, discipline course. I was a math major in undergrad and am also a math major for grad...so I had the pleasure 🙃 of taking upper-level statistics courses. 

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     Properties of expectation
        ✔️     Properties of variance
     

Here is what WMP! #67 says...

Happy solving!

P.S. There is nothing wrong with looking it up, even if you're not familiar with it.

Check back on Saturday, December 11th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Let's jump into this solution!

Hopefully, you've gotten a chance to look at the properties for expectation and variance involving random variables. If so, then you may have noticed that for part A, there were no formulas for expectation that involved variance. However, if you saw the properties for variance, then you should've seen a formula that involved expectation. That variance formula was taken and rearranged, so that expectation could be isolated.

I am aware that in isolating E(X), there should be a negative value also. I have chosen not to use it, since all of the givens are positive.

Parts B and C, are more straightforward when it comes to using the properties. Part B is dependent on the result from Part A.

▪️ Have you ever worked with expectation and variance in this way before??

▪️ Let me know what you thought about this week's problem in the comments section. 

Thanks for solving with me this week!
WMP! #68 is up next...the last WMP of 2021. 😥

Cheers!

The Younge Lady