Let X be a random variable with a probability density What i

Let X be a random variable with a probability density What is the value of c? Find P{1/2

Solution

a)

c Integral [4x - 2x^2]dx |(0,2) = c [2x^2 - 2x^3/3] |(0,2) = 1

c[2(2)^2 - 2(2)^3/3] = 1

c(8/3) = 1

c = 3/8 [answer]

b)

P(1/2 < x < 3/2) = (3/8)[2x^2 - 2x^3/3]|(1/2,3/2)

= (3/8){[2(3/2)^2 - 2(3/2)^3/3] - [2(1/2)^2 - 2(1/2)^3/3]}

= 11/16 [ANSWER]