# Question: Suppose X and Y are both integer valued random variables Let p i j

Suppose X and Y are both integer-valued random variables. Let

p(i|j) = P(X = i|Y = j)

and

q(j|i) = P(Y = j|X = i)

Show that

p(i|j) = P(X = i|Y = j)

and

q(j|i) = P(Y = j|X = i)

Show that

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

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}. A rectangular array of mn numbers arranged in n rows, each consisting of m columns, is said to contain a saddlepoint if there is a number that is both the minimum of its row and the maximum of its column. For instance, in ...Let X(1) ≤ X(2) ≤ . . . ≤ X(n) be the ordered values of n independent uniform (0, 1) random variables. Prove that for 1 ≤ k ≤ n + 1, P{X(k) − X(k−1) > t} = (1 − t)n where X(0) ≡ 0, X(n+1) ≡ t. Consider n independent flips of a coin having probability p of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if n = 5 and the outcome is HHTHT, then there ...We say that X is stochastically larger than Y, written X ≥st Y, if, for all t. P{X > t} ≥ P{Y > t} Show that if X ≥st Y, then E[X] ≥ E[Y] when (a) X and Y are nonnegative random variables; (b) X and Y are arbitrary ...Post your question