Consider the following probability density function for the random variable X :
f(x) = Kx 0 < x < 2
f(x) = K(4 - x) 2 < x < 4
0 else
a. Find the value of K for which f(x) is a probability density function
I found K to be 1/4
b. Find the mean of X
c. Find the variance of X
d. Find the cumulative distribution function of X