The discrete random variable X has probability function
k(2 –x), x= 0, 1, 2,
P(X = x) = k(x–2), x= 3,
0, otherwise,
where k is a positive constant.
(a) Show that k = 0.25.
(b) Find E(X) and show that E(X ) = 2.5.
(c) Find Var(3X – 2).
Two independent observations X1 and X2 are made of X.
(d) Show that P(X1 + X2 = 5) = 0.
(e) Find the complete probability function for X1 + X2.
(f) Find P(1.3 = X1 + X2 = 3.2).
Please can anyone tell me how to do the parts d,e,f? i have done the first 3 parts but these last three are confusing. Ive got the answers for this but in the MS they havent explained anything.
anyways this is wht written in the MS.
How and wht the hell they did? and wht is the logic behind it?
(d) P(X1 + X2) = P(X1 = 3 X2 = 2) + P(X1 = 2 X2 = 3) = 0 + 0 = 0
Let Y = X1 + X2 y 0 1 2 3 4 5 6
(e)
P(Y = y) 0.25 0.25 0.0625 0.25 0.125 0 0.0625
(f) P(1.3 X1 + X2 3.2) = P(X1 + X2 = 2) + P(X1 + X2 = 3)
= 0.0625 + 0.25 = 0.3125
Please help me out here.