Question: Please help with Question 5b and Question 6. QUESTION 5 (a) Let U1, U2, ..., U15 be i.i.d. uniform on the interval (0, 1). Consider

Please help with Question 5b and Question 6.

QUESTION 5 (a) Let U1, U2, ..., U15 be i.i.d. uniform on the interval (0, 1). Consider the order statistics U 4) and U(10), that is, the fourth-smallest and tenth-smallest of U1, U2, . .., U15. Find the joint density of U(4) and U(10). (b) Let U be uniform on the interval (0, 1) and let Y = (1 - U)-0.5. Find the density of Y. QUESTION 6 Suppose there are 200 lottery tickets of which 15 are winning tickets. Suppose each of 20 people buys 10 lottery tickets as follows: the first person buys a simple random sample of 10 tickets, then the next person buys a simple random sample of 10 out of the remaining 190 tickets, and so on. Let X be the number of people who get no winning tickets. (a) Find E(X). (b) Find Var(X)

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