just need ans for the wrong one. ## Understanding Joint PMF with a Service Station ExampleA service station has both self-service and full-service islands. On each island, a single regular unleaded pump with two hoses is available. 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 probability mass function (pmf) of \( X \) and \( Y \) is given in the following table:| \( p(x,y) \) | \( y = 0 \) | \( y = 1 \) | \( y = 2 \) ||--------------|------------|------------|------------|| \( x = 0 \) | 0.10 | 0.03 | 0.02 || \( x = 1 \) | 0.06 | 0.20 | 0.08 || \( x = 2 \) | 0.06 | 0.14 | 0.31 |### Calculations and Interpretations(a) **Probability of \( P(X = 1 \text{ and } Y = 1) \):**\[ P(X = 1 \text{ and } Y = 1) = 0.20 \](b) **Probability of \( P(X \leq 1 \text{ and } Y \leq 1) \):**\[ P(X \leq 1 \text{ and } Y \leq 1) = 0.39 \](c) **Description and Probability of the Event \( \{X \neq 0 \text{ and } Y \neq 0\} \):**- **Description:** At least one hose is in use at both islands.- **Computed Probability:** \[ P(X \neq 0 \text{ and } Y \neq 0) = 0.73 \](d) **Marginal PMF Calculations:**- **Marginal PMF of \( X \), \( p_X(x) \):** | \( x \) | 0 | 1 | 2 | |--------|------|------|------| | \( p_X(x) \) | 0.15 | 0

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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) у 0 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.06 0.14 0.31 (a) What is P(X= 1 and Y= 1)? P(X= 1 and Y = 1) = 0.20 (b) Compute P(X ≤ 1 and Y s 1). P(X ≤ 1 and Y≤ 1) = 0.39 (c) Give a word description of the event (X = 0 and Y 0). O One hose is in use on both islands. At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on one island. Compute the probability of this event. P(X 0 and Y 0) 0.73 (d) Compute the marginal pmf of X. 0 Px(x) 0.15 Compute the marginal pmf of Y. 0.34 0 2 Py(y) 0.22 Using px(x), what is P(X ≤ 1)? P(X ≤ 1) = 0.5 X ✓ 0.37 1 0.51 0.41 2 2

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) у 0 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.06 0.14 0.31 (a) What is P(X= 1 and Y= 1)? P(X= 1 and Y = 1) = 0.20 (b) Compute P(X ≤ 1 and Y s 1). P(X ≤ 1 and Y≤ 1) = 0.39 (c) Give a word description of the event (X = 0 and Y 0). O One hose is in use on both islands. At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on one island. Compute the probability of this event. P(X 0 and Y 0) 0.73 (d) Compute the marginal pmf of X. 0 Px(x) 0.15 Compute the marginal pmf of Y. 0.34 0 2 Py(y) 0.22 Using px(x), what is P(X ≤ 1)? P(X ≤ 1) = 0.5 X ✓ 0.37 1 0.51 0.41 2 2

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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