Suppose X and Y are iid Uniform[0,1] random variables.

Please explain in detail how you get the answer for each question. Thanks.

V1X+/v (7) Suppose X and Y are iid Uniform[0,1] random variables. Let U = X and the correct answer in each of parts (a), (b), (d), (e) and show your war (c). (a) P(V U S 1/2) = ) Krill EggUA'U' ; Circle in part Jacobsian factor for ( u, v ) 1(x , " ) is equal to 1. 0, 1/8, (1/2. 9 (b) The domain D where the joint density f(,v) (u, v) is defined is given by . D = {(u, v) : 0 1 2 u separately. Fun (,v ) = 1 4 ( ", V)ED For ofvel : friv) = 1 du = v For 16052 : 1. du = 2-v 5 - 1 U 2 (d) P(U > 1/2 | V = 1) = 1/2, f culus = It, for osusral 1, 1/4. (e) E(V | U = 1) = I for FrisuEr ( 2-V 1 V A 1/2, 1 , 3/2. D 2\f