Chapter 15.5, Problem 5P

Set up sample spaces for Problems 1 to 7 and list next to each sample point the value of the indicated random variable x, and the probability associated with the sample point. Make a table of the different values $x_i$ of $x$ and the corresponding probabilities $p_i=f\left(x_i\right)$ Compute the mean, the variance, and the standard deviation for x. Find and plot the cumulative distribution function. $F(x).$

A random variable $x$ takes the values 0,1,2,3, with probabilities $\frac{5}{12},\frac{1}{3},\frac{1}{12},\frac{1}{6}.$