Question

Let the random variables X and Y have joint PMF Px,y(x, y) x + y 32 2 = for - 1, 2 and y = 1, 2, 3, 4. (a) Find the correlation coefficient of X and Y. (b) Find E[Y|X] (c) Compute P(1

Answer 1

To find the correlation coefficient of X and Y, we first need to calculate the means, standard deviations, and covariance. E[Y|X] can be found using the conditional probability formula. P(1<X<2) can be computed by summing the probabilities of the relevant combinations of X and Y.

Step-by-step explanation:

To find the correlation coefficient of X and Y, we first need to calculate the means (E[X] and E[Y]), the standard deviations (σX and σY), and the covariance (Cov(X, Y)). The correlation coefficient (ρ) is then given by the formula: ρ = Cov(X, Y) / (σX * σY). To find E[Y|X], we use the conditional probability formula: E[Y|X] = Σ(y * P(Y=y|X)) for all possible values of y. To compute P(1<X<2), we add up the probabilities of each combination of X and Y that satisfies the condition 1<X<2.