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Refer to Part B of Table 2.30 for the conditional distribution of the numbe network failures M given network age A. Let Pr (A = 0) = 0.5; that is, you your room 50% of the time. a. Compute the probability of three network failures, Pr (M = 3). b. Use Bayes' rule to compute Pr (A = 0|M = 3). c. Now suppose you work in your room one-fourth of the time, so Pr (4 (0) -0.25. Use Baves' rule to compute Pr(4-OLM. 3)

Refer to Part B of Table 2.30 for the conditional distribution of the numbe network failures M given network age A. Let Pr (A = 0) = 0.5; that is, you your room 50% of the time. a. Compute the probability of three network failures, Pr (M = 3). b. Use Bayes' rule to compute Pr (A = 0|M = 3). c. Now suppose you work in your room one-fourth of the time, so Pr (4 (0) -0.25. Use Baves' rule to compute Pr(4-OLM. 3)

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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## Exercise 2.28 Refer to Part B of **Table 2.3** for the conditional distribution of the number of network failures \( M \) given network age \( A \). Let \( \Pr(A = 0) = 0.5 \); that is, you work in your room 50% of the time. a. Compute the probability of three network failures, \( \Pr(M = 3) \). b. Use Bayes' rule to compute \( \Pr(A = 0 \mid M = 3) \). c. Now suppose you work in your room one-fourth of the time, so \( \Pr(A = 0) = 0.25 \). Use Bayes' rule to compute \( \Pr(A = 0 \mid M = 3) \).
Transcribed Image Text:## Exercise 2.28 Refer to Part B of **Table 2.3** for the conditional distribution of the number of network failures \( M \) given network age \( A \). Let \( \Pr(A = 0) = 0.5 \); that is, you work in your room 50% of the time. a. Compute the probability of three network failures, \( \Pr(M = 3) \). b. Use Bayes' rule to compute \( \Pr(A = 0 \mid M = 3) \). c. Now suppose you work in your room one-fourth of the time, so \( \Pr(A = 0) = 0.25 \). Use Bayes' rule to compute \( \Pr(A = 0 \mid M = 3) \).
**Table 2.3: Joint and Conditional Distributions of Number of Wireless Connection Failures (M) and Network Age (A)** ### A. Joint Distribution | | M = 0 | M = 1 | M = 2 | M = 3 | M = 4 | Total | |------------------|-------|-------|-------|-------|-------|-------| | Old network (A = 0) | 0.35 | 0.065 | 0.05 | 0.025 | 0.01 | 0.50 | | New network (A = 1) | 0.45 | 0.035 | 0.01 | 0.005 | 0.00 | 0.50 | | Total | 0.80 | 0.10 | 0.06 | 0.03 | 0.01 | 1.00 | ### B. Conditional Distributions of M given A | | M = 0 | M = 1 | M = 2 | M = 3 | M = 4 | Total | |--------------------------|-------|-------|-------|-------|-------|-------| | Pr(M | A = 0) | 0.70 | 0.13 | 0.10 | 0.05 | 0.02 | 1.00 | | Pr(M | A = 1) | 0.90 | 0.07 | 0.02 | 0.01 | 0.00 | 1.00 | **Explanation:** - The table consists of two parts: - **Joint Distribution**: Represents probabilities of connection failures (M) with respect to network age (A). - Old network (A = 0) shows higher probabilities of low values of M, indicating fewer connection failures in such instances. - New network (A = 1) also tends to have lower values of M, with a very low probability of significant failures (M > 2). - Total column sums indicate the probability distribution for each network type. - **Conditional Distribution**: Shows probabilities of M occurring given the condition of A, i.e., the type of network. - For old
Transcribed Image Text:**Table 2.3: Joint and Conditional Distributions of Number of Wireless Connection Failures (M) and Network Age (A)** ### A. Joint Distribution | | M = 0 | M = 1 | M = 2 | M = 3 | M = 4 | Total | |------------------|-------|-------|-------|-------|-------|-------| | Old network (A = 0) | 0.35 | 0.065 | 0.05 | 0.025 | 0.01 | 0.50 | | New network (A = 1) | 0.45 | 0.035 | 0.01 | 0.005 | 0.00 | 0.50 | | Total | 0.80 | 0.10 | 0.06 | 0.03 | 0.01 | 1.00 | ### B. Conditional Distributions of M given A | | M = 0 | M = 1 | M = 2 | M = 3 | M = 4 | Total | |--------------------------|-------|-------|-------|-------|-------|-------| | Pr(M | A = 0) | 0.70 | 0.13 | 0.10 | 0.05 | 0.02 | 1.00 | | Pr(M | A = 1) | 0.90 | 0.07 | 0.02 | 0.01 | 0.00 | 1.00 | **Explanation:** - The table consists of two parts: - **Joint Distribution**: Represents probabilities of connection failures (M) with respect to network age (A). - Old network (A = 0) shows higher probabilities of low values of M, indicating fewer connection failures in such instances. - New network (A = 1) also tends to have lower values of M, with a very low probability of significant failures (M > 2). - Total column sums indicate the probability distribution for each network type. - **Conditional Distribution**: Shows probabilities of M occurring given the condition of A, i.e., the type of network. - For old
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