round your answer to 3 decimal points.

A continuous random variable X has the following PDF:

Osxs 2

f(x)

0

otherwise

(a) Find the value of k to make f(x) a legitimate probability density function.

={*{(x – 23]

(b) What is the probability that X is smaller than 1.3?

(c) Find the mean of X.

(d) Find the variance of X.

(e) What is the probability that X is within 0.3 of its mean?