Suppose two events A and B are two independent events with P(A) > P(B) and P(A...
Help please! Suppose two events A and B are two independent events with P(A) > P(B) and P(AU B) = 0.626 and PAn B)-0.144, determine the values of P(A) and P(B). 9.
B] <P[AP[B], and of two events A and B Give an example of two events such that P[ A with P[An B] > P[A]P[B].
Suppose that A1,A2,.., Ak are mutually exclusive events and P(B)>0. Prove that
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
1. Consider two independent events, A and B, where 0< P(A) <1,0< P(B)< 1. Prove that A and B' are independent as well.
1. Use the formula P(A) PABP(B) + P(AlBc)P(B") to prove that if P(AB) P (AlBc) then A and B are independent. Then prove the converse (that if A and B are independent then P(AIB)- P(ABe). [Assume that P(B) > 0 and P(B) > 0.]
Consider two independent events, A and B, where 0くP(A) < 1,0くP(8)く1. Prove that A' and B' are independent as well.
Assume that X and Y are independent and follow normal distributions with Hx (a) evaluate P(X +Y > 24) (2pt) (b) that P(z < X-Y < 10) = 0.2 (3pt) find r such
4. Suppose A, B, C are events such that P(A), P(B), P(C) a. If (A, B, C) are independent, show that P(AU BUC)- b. If A, B, C are only pairwise independent, show that 17 24 SHA UBUC)<19 24
PROB5 Let U and V be independent r.v's such that the p.d.f of U is fu(u) = { 2 OSU< 27, otherwise. and the p.d.f'of2 is Seu, v>0, fv (v otherwise. Let X = V2V cos U and Y = 2V sin U. Show that X and Y are independent standard normal variables N(0,1).