Thread: Density

Suppose that X is a random variable whose density is f(x) = 1 / [2*(1 + |x|)^2] , (- inf < x< inf)

a) Draw the graph of f(x)
b) Find P(-1 < X < 2)
c) Find P(|X| > 1)
d) Is E(X) defined?

So I don't know about the other parts, but for part b is it just something like the integral from -1 to 2 of f(x)? Thanks for any help!!

Originally Posted by bart203

Suppose that X is a random variable whose density is f(x) = 1 / [2*(1 + |x|)^2] , (- inf < x< inf)

a) Draw the graph of f(x)
b) Find P(-1 < X < 2)
c) Find P(|X| > 1)
d) Is E(X) defined?

So I don't know about the other parts, but for part b is it just something like the integral from -1 to 2 of f(x)? Thanks for any help!!

Yes.

For each part, just apply the usual definition and crank out the calculation. Note that |x| = x for x > 0 and -x for x < 0. Please show all your work and say where you get stuck if you need more help.