You have prepared 10 types of treats for your 5 cats. You don’t know which treat...

You have prepared 10 types of treats for your 5 cats. You don’t know which treat each of your cats will

go for, so you have bought for each type enough treats for all your cats. Assume that each cat is equally

likely to choose any type of treats, and let X be the number of pairs of cats that will choose the same

type of treats. Compute E(X) and Var(X).

(Hint: consider events Ai,j that the ith and jth cats will choose the same type of treats.)

Expert Solution

A(i, j) pair that ith and jth cat choose same treat

Each cat choose treat equally likey with prob 5/10=0.5

P(Ai.j)=P(Ai)P(Aj)=0.5*0.5=0.25

For example P(A12) =0.25

A12, A13, A14, A15 there 4 such pairs of cats those will choose same treat with probability 0.25

We get E(X) =2.50

Variance (X) =1.25

Solution file is attached go through it

Thanks

orchestra answered 11 months ago

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You have prepared 10 types of treats for your 5 cats. You don’t know which treat...

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