Let (X,Y) have the joint probability mass function f(x,y)=begincasesdbinomx+1ydbinom16x(1/6)^y(5/6)^x+1-y(1/2)^16,&y=0,1,…,x+1; x=0,1,…,160,&otherwiseendcases Then which of the following statements is/are TRUE?

Q36Section B (Section B)36 of 60

Moments of a binomial mixture

Let $(X,Y)$ have the joint probability mass function $f(x,y)=\begin{cases}\dbinom{x+1}{y}\dbinom{16}{x}\left(\dfrac{1}{6}\right)^{y}\left(\dfrac{5}{6}\right)^{x+1-y}\left(\dfrac{1}{2}\right)^{16},&y=0,1,…,x+1; x=0,1,…,16\\0,&\text{otherwise}\end{cases}$ Then which of the following statements is/are TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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