# Project #19577 - Stas for MORA

Like stated before, deadline is final and can't be extended. Thank you!

I need the following 8 problems solved:

3) Let U, V, W, X, Y, Z be six independent and identically distributed

geometric random variables with parameter p, where 0 < p < 1. Let

S = max{U,V,W,X,Y,Z}. Find the p.m.f. of S and also find E(S).

(There is plenty of time for evolution)

4) Let U, V, X, Y, Z be five independent and identically distributed

exponential random variables with parameter c, where 0 < c. Let W

= medium of U,V,X,Y,Z. Find the pmf of W and also find E(W) and

Var(W).

5) 3 players A, B, and C take turns at a game according to the

following rules. At the start A and B play while C is out. The

loser is replaced by C and at the second trial the winner plays

against C while the loser is out. The game continues in this way

until a player wins twice in succession, thus becoming the winner

of the game. What is the probability that Player A will be the

winner? What is the probability that Player C will be the winner?

(assume in each match, A has 0.55 chance to beat B, and 0.45 chance

to beat C, B has 0.55 chance to beat C.)

6) Let U be a geometric random variable with p = 0.3, V be a geometric

random variable with p = 0.3, X be a geometric random variable with p

= 0.5, Y be a geometric random variable with p = 0.4. Let U, V, X, Y

be independent and W = U + V + X + Y. Find P(W = k) for k = 5,6,7.

19) A pharmaceutical salesman claimed that the side effect of their new drug

is at most 5%. If you give the drug to 10,000 patients and 546 patients

are getting side effect. If the significant level is 5%, will you accept

her (or his) claim? lf not, then at what significant level you will accept

her (or his) claim? Also compute the p—value.

21)Let S, T, U be i.i.d. exponential distribution random variables with

Θ = 10. Let X = min(S,T,U) and Y = max(S,T,U). Find E(X), E(Y),

Var(X), Var(Y) and Cov(X,Y).

22) Let X, Y, and Z be three random variables distributed uniformly over

the interval [O,1O]. Let A be the event that X, Y, and Z form a

triangle, ie., X + Y > Z, X + Z > Y, and Y + Z > X. Prove that P(A)

= 0.5.

23)Let X and Y be two random variables distributed uniformly over

the interval [O,1O]. They split the interval [O,1O] into three

parts, a, b, C. Let B be the event that a, b, and c form a triangle,

ie., a + b > x, a + c > b, and b + c > a. Prove that P(B) : 0.25;

 Subject Mathematics Due By (Pacific Time) 12/13/2013 12:00 am
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