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P(X ≤ 1 and Y≤ 1) = 0.41 (c) Give a word description of the event {X = 0 and Y# 0}. At most one hose is in use at both islands. One hose is in use on both islands. One hose is in use on one island. At least one hose is in use at both islands. Compute the probability of this event. P(X + 0 and Y# 0) = 0.9 X (d) Compute the marginal pmf of X. Px(x) 0 у Py(Y) Compute the marginal pmf of Y. 1 0 1 Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = 2 2

P(X ≤ 1 and Y≤ 1) = 0.41 (c) Give a word description of the event {X = 0 and Y# 0}. At most one hose is in use at both islands. One hose is in use on both islands. One hose is in use on one island. At least one hose is in use at both islands. Compute the probability of this event. P(X + 0 and Y# 0) = 0.9 X (d) Compute the marginal pmf of X. Px(x) 0 у Py(Y) Compute the marginal pmf of Y. 1 0 1 Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = 2 2

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Only the part c and d needs to be solved
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let \( X \) denote the number of hoses being used on the self-service island at a particular time, and let \( Y \) denote the number of hoses on the full-service island in use at that time. The joint pmf of \( X \) and \( Y \) appears in the accompanying tabulation. | \( p(X, Y) \) | \( 0 \) | \( 1 \) | \( 2 \) | |------------|-------|-------|-------| | \( x = 0 \) | 0.10 | 0.05 | 0.02 | | \( x = 1 \) | 0.06 | 0.20 | 0.08 | | \( x = 2 \) | 0.05 | 0.14 | 0.30 | **Questions and Solutions:** (a) What is \( P(X = 1 \text{ and } Y = 1) \)? \( P(X = 1 \text{ and } Y = 1) = \text{0.20} \) ✓ (b) Compute \( P(X \leq 1 \text{ and } Y \leq 1) \). \( P(X \leq 1 \text{ and } Y \leq 1) = \text{0.41} \) ✓ (c) Give a word description of the event \( \{X \neq 0 \text{ and } Y \neq 0\} \). Options: - At most one hose is in use at both islands. - One hose is in use on both islands. - One hose is in use on one island. - At least one hose is in use at both islands. Correct Answer: At least one hose is in use at both islands. ✓ Compute the probability of this event. \( P(X \neq 0 \text{ and } Y \neq 0) = \text{0.9} \) ✗ (d) Compute the marginal pmf of \( X \). | \( x \) | 0 | 1 | 2 | |---------|------|------|------|
Transcribed Image Text:A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let \( X \) denote the number of hoses being used on the self-service island at a particular time, and let \( Y \) denote the number of hoses on the full-service island in use at that time. The joint pmf of \( X \) and \( Y \) appears in the accompanying tabulation. | \( p(X, Y) \) | \( 0 \) | \( 1 \) | \( 2 \) | |------------|-------|-------|-------| | \( x = 0 \) | 0.10 | 0.05 | 0.02 | | \( x = 1 \) | 0.06 | 0.20 | 0.08 | | \( x = 2 \) | 0.05 | 0.14 | 0.30 | **Questions and Solutions:** (a) What is \( P(X = 1 \text{ and } Y = 1) \)? \( P(X = 1 \text{ and } Y = 1) = \text{0.20} \) ✓ (b) Compute \( P(X \leq 1 \text{ and } Y \leq 1) \). \( P(X \leq 1 \text{ and } Y \leq 1) = \text{0.41} \) ✓ (c) Give a word description of the event \( \{X \neq 0 \text{ and } Y \neq 0\} \). Options: - At most one hose is in use at both islands. - One hose is in use on both islands. - One hose is in use on one island. - At least one hose is in use at both islands. Correct Answer: At least one hose is in use at both islands. ✓ Compute the probability of this event. \( P(X \neq 0 \text{ and } Y \neq 0) = \text{0.9} \) ✗ (d) Compute the marginal pmf of \( X \). | \( x \) | 0 | 1 | 2 | |---------|------|------|------|
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