Question

5. A) The joint PMF of the random variables X and Y is given by the following table: | | y = 3 | c | c | 2c | |---|---|---|---|---| | | y = 2 | 2c | 0 | 4c | | | y = 1 | 3c | c | 6c | | | | x = 1 | x = 2 | x = 3 | i. Find the value of the constant c. ii. Find PY(2). B) Let fX,Y(x, y) = {1/2(x + y) for 0 ? x ? 1, 1 ? y ? 2; 0 otherwise i. Check that fX,Y(x, y) is a joint density ii. What is P(X ? 1/2)

          5.
A) The joint PMF of the random variables X and Y is given by the following table:
| | y = 3 | c | c | 2c |
|---|---|---|---|---|
| | y = 2 | 2c | 0 | 4c |
| | y = 1 | 3c | c | 6c |
| | | x = 1 | x = 2 | x = 3 |
i. Find the value of the constant c.
ii. Find PY(2).
B) Let fX,Y(x, y) = {1/2(x + y) for 0 ? x ? 1, 1 ? y ? 2; 0 otherwise
i. Check that fX,Y(x, y) is a joint density
ii. What is P(X ? 1/2)

5.
A) The joint PMF of the random variables X and Y is given by the following table:
| | y = 3 | c | c | 2c |
|—|—|—|—|—|
| | y = 2 | 2c | 0 | 4c |
| | y = 1 | 3c | c | 6c |
| | | x = 1 | x = 2 | x = 3 |
i. Find the value of the constant c.
ii. Find PY(2).
B) Let fX,Y(x, y) = 1/2(x + y) for 0 ? x ? 1, 1 ? y ? 2; 0 otherwise
i. Check that fX,Y(x, y) is a joint density
ii. What is P(X ? 1/2)

Added by Meghan B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

08/26/2023

Step 1

To find the value of the constant c, we need to use the fact that the sum of all probabilities in a joint PMF must be equal to 1. So, we have: 2c + 1 = 2 1 + 3c = 1 Solving for c, we get: c = 1/3 Show more…

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A) The joint PMF of the random variables X and Y is given by the following table: i. Find the value of the constant c. ii. Find PY(2). B) Let fX,Y(x, y) = {1/2(x + y) for 0 ≤ x ≤ 1, 1 ≤ y ≤ 2; 0 otherwise i. Check that fX,Y(x, y) is a joint density ii. What is P(X ≥ 1/2)