Probability density function: f(x) = {k (2 +x^2 -x) -1 <= x <= 2, 0 otherwise

[Hev99]

Hi, I have this question about pdf:
Suppose X be a continuous random variable with the pdf:
f(x) = {k (2 +x^2 -x) -1 <= x <= 2
0 otherwise
I need to find the value of k, which is a positive constant and then obtain the cumulative distribution function (F (x)) of X.
Can someone help please?

 

[HallsofIvy]

Hi, I have this question about pdf:
Suppose X be a continuous random variable with the pdf:
f(x) = {k (2 +x^2 -x) -1 <= x <= 2
0 otherwise
I need to find the value of k, which is a positive constant and then obtain the cumulative distribution function (F (x)) of X.
Can someone help please?

A basic property of a probability distribution is that the total probability (the probability that something in the domain happens) is 1. That is \(\displaystyle \int_{-1}^2 k(2+ x^2- x)dx= 1\). Do the integration and solve for k.

The cumulative distribution function is \(\displaystyle F(X)= \int_{-1}^X k(2+ x^2- x)dx\).