## Question

# There are 20 different pairs of shoes. Pick at random 10 shoes . Let X be the number of paired shoes, M be the number

There are 20 different **pairs** of shoes. Pick at random **10 shoes**. Let X be the number of paired shoes, M be the number of shoes that are left-foot, N be the number of shoes that are right-foot.

(a)Find the distribution of X. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula

(b)Let Y = M - N. Give all possible values of Y. Find the distribution of Y. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula.

(c)let Z = |Y|, compute E(X), Var(X), E(Z) and Var(Z). Show your problem-solving process (not just the answer), keep 2 decimal places for E(X) and E(Z), and use the approximate values for the calculations of Var(X) and Var(Z).

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