For Question 2 on this document:

https://www.coursehero.com/file/26464217/HW-4-solutionspdf/#/doc/qa

Is Number 2 correct for the E(X)?

Solution: The mean is OO E(X) = > KP(X - k) = c> ope k=1 k=1 1 - p To get the variance, let's first find E(X?) (using LOTUS): DO E(X2) = SKIP(X = k) = c kp* . k=1 K=1 We computed a similar sum when deriving the mean of a Geometric; specifically, Exam- ple 4.3.5 shows that DO Cup* = PE kp k-1 P k=1 k-1 (1-p)?' Therefore, Var(X ) = cp c2 p2 op - cap2 (1 -p)2 (1 - p)2 (1 - p)2