Question

Problem 1 Consider two random variables X and Y with joint PMF given in Table 5.4 Joint PMF of X and Y in Problem 1 | | Y = 1 | Y = 2 | | :--- | :---: | :---: | | X = 1 | 1/3 | 1/12 | | X = 2 | 1/6 | 0 | | X = 4 | 1/12 | 1/3 | a. Find P(X ? 2, Y > 1). b. Find the marginal PMFs of X and Y. c. Find P(Y = 2|X = 1). d. Are X and Y independent?

          Problem 1
Consider two random variables X and Y with joint PMF given in Table 5.4
Joint PMF of X and Y in Problem 1

| | Y = 1 | Y = 2 |
| :--- | :---: | :---: |
| X = 1 | 1/3 | 1/12 |
| X = 2 | 1/6 | 0 |
| X = 4 | 1/12 | 1/3 |

a. Find P(X ? 2, Y > 1).
b. Find the marginal PMFs of X and Y.
c. Find P(Y = 2|X = 1).
d. Are X and Y independent?

Problem 1
Consider two random variables X and Y with joint PMF given in Table 5.4
Joint PMF of X and Y in Problem 1

| | Y = 1 | Y = 2 |
| :— | :—: | :—: |
| X = 1 | 1/3 | 1/12 |
| X = 2 | 1/6 | 0 |
| X = 4 | 1/12 | 1/3 |

a. Find P(X ? 2, Y > 1).
b. Find the marginal PMFs of X and Y.
c. Find P(Y = 2|X = 1).
d. Are X and Y independent?

Added by Carla P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Federico Castro

Step 1

Since X can only take the values 1 and 4, and Y can only take the values 1 and 2, the only possible combination that satisfies the condition is when X = 1 and Y = 2. So, we need to find the probability P(X = 1, Y = 2) from the table. b. Show more…

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Consider two random variables X and Y with joint PMF given in Table 5.4. Joint PMF of X and Y in Problem: Y = 1 X = 2 Y = 1 X = 4 a. Find P(X < 2, Y > 1). b. Find the marginal PMFs of X and Y. c. Find P(Y = 2X = 4). d. Are X and Y independent?