Every day, the 30 employees at an auto plant each has probability 0.03 of having one accident and zero probability of having more than one accident. Given there was an accident, the probability of it being major is 0.01. All other accidents are minor. The numbers and severities of employee accidents are mutually independent. Let X and Y represent the numbers of major accidents and minor accidents, respectively, occurring in the plant today for a single employee. Denote by p(x, y) the joint mass distribution of the random variables X and Y

(a) Compute pi (0, 0); p (1, 0); p (0, 1) and p, (1, 1). (b) Deduce the joint moment-generating function, May(s, t) of the ran- dom variables X and Y. (c) Let V and W represent the total numbers of major accidents and minor accidents, respectively, occurring in the plant today for all the 30 em- ployees. Compute the joint moment-generating function, My,w(s, t). Substantiate your