Given the probability distributions shown below, complete the following parts. a. Compute the expected value for each distribution A and B.b. Compute the standard deviation for distribution A and B.c. What is the probability that x will be at least 3 in Distribution A and Distribution B?. ### Comparing Discrete DistributionsThis analysis presents two discrete probability distributions, A and B. Each distribution provides the probability $ P(X = x_i) $ for different $ x_i $ values ranging from 0 to 4.#### Distribution A- **$ x_i = 0 $:** Probability $ P(X = 0) = 0.06 $- **$ x_i = 1 $:** Probability $ P(X = 1) = 0.11 $- **$ x_i = 2 $:** Probability $ P(X = 2) = 0.15 $- **$ x_i = 3 $:** Probability $ P(X = 3) = 0.21 $- **$ x_i = 4 $:** Probability $ P(X = 4) = 0.47 $#### Distribution B- **$ x_i = 0 $:** Probability $ P(X = 0) = 0.47 $- **$ x_i = 1 $:** Probability $ P(X = 1) = 0.21 $- **$ x_i = 2 $:** Probability $ P(X = 2) = 0.15 $- **$ x_i = 3 $:** Probability $ P(X = 3) = 0.11 $- **$ x_i = 4 $:** Probability $ P(X = 4) = 0.06 $### Analysis- **Distribution A** gradually increases in probability as $ x_i $ increases, reaching a peak at $ x_i = 4 $.- **Distribution B** shows a reverse pattern, with the highest probability at $ x_i = 0 $ and decreasing as $ x_i $ increases. This comparison illustrates contrasting probability patterns between the two distributions, highlighting different tendencies of occurrence for these discrete events.

The probability distribution of is given by, 00.0610.1120.1530.2140.47The probability distribution…

Given the probability distributions shown below, complete the following parts. a. Compute the expected value for each distribution A and B. b. Compute the standard deviation for distribution A and B. c. What is the probability that x will be at least 3 in Distribution A and Distribution B?.

Given the probability distributions shown below, complete the following parts. a. Compute the expected value for each distribution A and B. b. Compute the standard deviation for distribution A and B. c. What is the probability that x will be at least 3 in Distribution A and Distribution B?.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Given the probability distributions shown below, complete the following parts.

a. Compute the expected value for each distribution A and B.

b. Compute the standard deviation for distribution A and B.

c. What is the probability that x will be at least 3 in Distribution A and Distribution B?.

### Comparing Discrete Distributions

This analysis presents two discrete probability distributions, A and B. Each distribution provides the probability $ P(X = x_i) $ for different $ x_i $ values ranging from 0 to 4.

#### Distribution A

- **$ x_i = 0 $:** Probability $ P(X = 0) = 0.06 $
- **$ x_i = 1 $:** Probability $ P(X = 1) = 0.11 $
- **$ x_i = 2 $:** Probability $ P(X = 2) = 0.15 $
- **$ x_i = 3 $:** Probability $ P(X = 3) = 0.21 $
- **$ x_i = 4 $:** Probability $ P(X = 4) = 0.47 $

#### Distribution B

- **$ x_i = 0 $:** Probability $ P(X = 0) = 0.47 $
- **$ x_i = 1 $:** Probability $ P(X = 1) = 0.21 $
- **$ x_i = 2 $:** Probability $ P(X = 2) = 0.15 $
- **$ x_i = 3 $:** Probability $ P(X = 3) = 0.11 $
- **$ x_i = 4 $:** Probability $ P(X = 4) = 0.06 $

### Analysis

- **Distribution A** gradually increases in probability as $ x_i $ increases, reaching a peak at $ x_i = 4 $.
- **Distribution B** shows a reverse pattern, with the highest probability at $ x_i = 0 $ and decreasing as $ x_i $ increases.

This comparison illustrates contrasting probability patterns between the two distributions, highlighting different tendencies of occurrence for these discrete events.

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