A random variable X has pdf a Sketch the pdf b Find the posi

A random variable X has pdf:

(a) Sketch the pdf

(b) Find the positive value c

(c) Find the probability that Pr[X > ?1]

(d) Find the probability that Pr[|X| ? 0.8]

(e) Find the probability that X > 1 or X < ?1.2.

(f) Find the cumulative distribution function of the random variable X

Solution

a) What is the value of c?
B)
We know that for f(x) to be a probability distribution
INTEGRATE f(x)dx = 1. integrate
f(x) with respect to x, set the result equal to 1 and solve for c

C) P(X > -1 ) = INTEGRATE F(X) FROM -1 TO INFINITY

F) FOR CUMULATIVE DISTRIBUTION

We HAVE to find F(x). To do that, integrate f(x) from the lower bound of the domain
on which f(x) IS NOT = 0 to x so we will get an expression in terms of x.