The PDF of a random variable X The PDF of a random variable

The PDF of a random variable X

The PDF of a random variable X4.42 The PDF of a random variable X is shown below. (a) Find the mean mX and the second moment of this random variable. (b) Determine the variance Sigma^2X. Determine Pr[mX-SigmaX leq X leq mX+SigmaX].

Solution

a) Mean = integral -1 to 1 of x(x+1)/4 + 1 to 3 of -x(x-3)/4= 1/6+5/6 =1

b) E(x^2) =1/6+ 3/2 = 5/3

Variance = 2/3

c) P(mx-sigmax<X <mx+sigmax) = P(1/3<x<5/3)

=5/18 + 5/18 = 5/9