A random variable X has probability density function given by

for −∞

a. Demonstrate that g_X(x) is a valid probability density function.

b. Calculate P(1.5

c. Determine a transformation that takes X to a Standard normal distribution and use statistical tables to verify your answer to part b.

You are given that Φ(1.75) = 0.95994 and Φ(0.25) = 0.59871.

gx(x) = 1 1 2/2m &p ( ;(;)') exp 22 2 2