# Question: Let A1 A2 An be arbitrary events

Let A1, A2, . . . ,An be arbitrary events, and define Ck = {at least k of the Ai occur}. Show that

Let X denote the number of the Ai that occur. Show that both sides of the preceding equation are equal to E[X].

Let X denote the number of the Ai that occur. Show that both sides of the preceding equation are equal to E[X].

**View Solution:**## Answer to relevant Questions

Let X have moment generating function M(t), and define ψ(t) = logM(t). Show that ψ′′(t)|t=0 = Var(X) Show that X is stochastically larger than Y if and only if E[f(X)] ≥ E[f(Y)] for all increasing functions f . Show that X ≥st Y, then E[f(X)] ≥ E[f(Y)] by showing that f(X) ≥st f(Y) and then using Theoretical ...A certain region is inhabited by r distinct types of a certain species of insect. Each insect caught will, independently of the types of the previous catches, be of type i with probability (a) Compute the mean number of ...If 101 items are distributed among 10 boxes, then at least one of the boxes must contain more than 10 items. Use the probabilistic method to prove this result. Cards from an ordinary deck are turned face up one at a time. Compute the expected number of cards that need to be turned face up in order to obtain (a) 2 aces; (b) 5 spades; (c) All 13 hearts.Post your question