# Question: In Example 5c we computed the conditional density of a

In Example 5c we computed the conditional density of a success probability for a sequence of trials when the first n + m trials resulted in n successes. Would the conditional density change if we specified which n of these trials resulted in successes?

## Relevant Questions

Suppose that X and Y are independent geometric random variables with the same parameter p. Without any computations, what do you think is the value of P{X = i|X + Y = n}? Imagine that you continually flip a coin having ...Let X1, X2, X3 be independent and identically distributed continuous random variables. Compute (a) P{X1 > X2|X1 > X3}; (b) P{X1 > X2|X1 < X3}; (c) P{X1 > X2|X2 > X3}; (d) P{X1 > X2|X2 < X3}. Suppose that F(x) is a cumulative distribution function. Show that (a) Fn(x) and (b) 1 − [1 − F(x)]n are also cumulative distribution functions when n is a positive integer. Let X1, . . . ,Xn be independent random ...If X and Y are independent continuous positive random variables, express the density function of (a) Z = X/Y and (b) Z = XY in terms of the density functions of X and Y. Evaluate the density functions in the special case ...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].Post your question