Question

Problem 2. Suppose the sample space S consists of the four points and the associated probabilities over the events are given by P(cu 1)-0.2, P(ω2)-0.3, P(ag)-0.1, P(04)-0.4 Define the random variable X1 by and the random variable X2 by X2(2) 5, (a) Find the probability distribution of X1 (b) Find the probability distribution of the random variable X1 +X2 Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 sX s 0.8)

Answer 1

solution: 3) Let X be r.v. with pat sosys Ex(y) = soya ocysl ow. a) Let 0=0.8 ve know Spalyldy = 1 Soyady + Sky ² df as o [ ]+[**] =1 $ [03-03 + [\-(0°) - 1 0018) + [1-0-88) 0.4096 tk 0.488 = 3 0.4886 = 2.590k K = 5.31] b) calf ofx falt) - Strakondy = $.8ypy fool 50% [8] com les ) Fx(t) = 38ť For 0. 84 = 1 ffor 0$decy? Falt1 = 5* saly? = 5:31 [89 Fxlt) = 177(+-0.93) 0.8 y Osusog drets Į Fx/t)=17702-08) 11.77(+30.83)

0.8 e) Plors 5X = 0.8) = fx or dy = 50.8yzdy -0-8 ( 7 Jove des [ 0.8 0.93 = (00458) 7P60.45X50-8 ) = 0.1195]