1) We roll two fair dice, a blue and red one, independently of each other. Let X be the number obtained upon the blue die minus the number obtained upon the red die. Draw histogram for its probability function and graph for its distribution function.
2) Let X be a discrete random variable with the probability function fX .
Determine formulas for the probability function and distribution function of Y =(X - a)^2, where a is an arbitrary constant.
3) Assume that the distribution of the radius R of stars has a density function fR. Find formulas for the density and the distribution function of their volume V = (4/3)R3p.
4) Let X be a random variable uniformly distributed on the interval [-1, 1], and Y = |X|. Find the density function and the distribution function of Y.
5) Let X be a binomial random variable with parameters p = 1/2 and n = 6. Find the probability function and the distribution function of Y = X^2 - 2X