Question

5-2. Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass function over the nine points with x = 1, 2, 3 and y = 1, 2, 3. Determine the following: (a) P(X = 1, Y < 3) (b) P(X = 1) (c) P(Y = 2) (d) P(X < 2, Y < 2) (e) E(X), E(Y), V(X), and V(Y) (f) Marginal probability distribution of X (g) Conditional probability distribution of Y given that X = 1 (h) Conditional probability distribution of X given that Y = 2 (i) E(Y | X = 1) (j) Are X and Y independent?

          5-2. Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass function over the nine points with x = 1, 2, 3 and y = 1, 2, 3. Determine the following:
(a) P(X = 1, Y < 3) (b) P(X = 1)
(c) P(Y = 2) (d) P(X < 2, Y < 2)
(e) E(X), E(Y), V(X), and V(Y)
(f) Marginal probability distribution of X
(g) Conditional probability distribution of Y given that X = 1
(h) Conditional probability distribution of X given that Y = 2
(i) E(Y | X = 1) (j) Are X and Y independent?

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5-2. Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass function over the nine points with x = 1, 2, 3 and y = 1, 2, 3. Determine the following:
(a) P(X = 1, Y < 3) (b) P(X = 1)
(c) P(Y = 2) (d) P(X < 2, Y < 2)
(e) E(X), E(Y), V(X), and V(Y)
(f) Marginal probability distribution of X
(g) Conditional probability distribution of Y given that X = 1
(h) Conditional probability distribution of X given that Y = 2
(i) E(Y | X = 1) (j) Are X and Y independent?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/05/2023

Step 1

Since the sum of all probabilities in a joint probability mass function must be equal to 1, we have: ∑∑f(x,y) = ∑∑e^(kxy) = e^k + e^(2k) + e^(3k) + e^(2k) + e^(4k) + e^(6k) + e^(3k) + e^(6k) + e^(9k) = 1 Simplifying this expression, we get: 2e^k + 2e^(2k) + Show more…

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5-2. Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass function over the nine points with x = 1, 2, 3 and y = 1, 2, 3. Determine the following: (a) P(X = 1, Y < 3) (b) P(X = 1) (c) P(Y = 2) (d) P(X < 2, Y < 2) (e) E(X), E(Y), V(X), and V(Y) (f) Marginal probability distribution of X (g) Conditional probability distribution of Y given that X = 1 (h) Conditional probability distribution of X given that Y = 2 (i) E(Y|X = 1) (j) Are X and Y independent?

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