Question

SALII II The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2(x + 2) f(x = 0<x<1 5 elsewhere a) Find the probability that more than 14 but fewer than 1/2 of the people contacted will respond to this type of solicitation. b) Find the expected value of X, E(X). [Note: E(X) is the mean value] c) Find the standard deviation.

Answer 1

Solution Given The density function 2(xt2) 5 elsewhere aFind the pvokooility that more han 4 hut fewer than 2 of the people contacted coll Yespoud to this type of Solicitat 4 J P x f(x) PCx) dx 4 2 t2) 9 i4 2 l2+2) d /2 2 2 t2 '/4 32 32 36-1 32 38 .1 160 19 80

b.) Find the eepectad value of x, ELx] 9 ECX) x fa) d 2CX+2) dx 5 в = 01533 Mean ECx)= c.) Find the Standard devratien 15 ECx 2-f(x) dx 5 3 2 4 22 1 11 60 30 12 Stondard-deviation ECXE 30 15 64 30 225 165-128 450 3T 450 0.2867