MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Probability Distribution Analysis #### Problem Statement Five males with an X-linked genetic disorder have one child each. The random variable \( x \) represents the number of children among the five who inherit the X-linked genetic disorder. The task is to determine whether the given table represents a probability distribution. If it is a probability distribution, calculate its mean and standard deviation. If it isn't, identify the unmet requirements. --- #### Table of Values | \( x \) | \( P(x) \) | |---------|-------------| | 0 | 0.027 | | 1 | 0.156 | | 2 | 0.317 | | 3 | 0.317 | | 4 | 0.156 | | 5 | 0.027 | --- #### Analysis Questions 1. **Does the table show a probability distribution? Select all that apply.** - [ ] A. Yes, the table shows a probability distribution. - [ ] B. No, the random variable \( x \) is categorical instead of numerical. - [ ] C. No, the random variable \( x \)'s number values are not associated with probabilities. - [ ] D. No, the sum of all the probabilities is not equal to 1. - [ ] E. No, not every probability is between 0 and 1 inclusive. 2. **Find the mean of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.** - [ ] A. \( \mu = \) ____ child(ren) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. 3. **Find the standard deviation of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.** - [ ] A. \( \sigma = \) ____ child(ren) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. --- #### Graphical Explanation This problem does not include graphs or diagrams. It involves evaluating the provided table to determine if it meets the criteria for a probability distribution, and subsequently calculating the mean and standard deviation. #### Notes for Understanding - A probability distribution
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Transcribed Image Text:### Probability Distribution Analysis #### Problem Statement Five males with an X-linked genetic disorder have one child each. The random variable \( x \) represents the number of children among the five who inherit the X-linked genetic disorder. The task is to determine whether the given table represents a probability distribution. If it is a probability distribution, calculate its mean and standard deviation. If it isn't, identify the unmet requirements. --- #### Table of Values | \( x \) | \( P(x) \) | |---------|-------------| | 0 | 0.027 | | 1 | 0.156 | | 2 | 0.317 | | 3 | 0.317 | | 4 | 0.156 | | 5 | 0.027 | --- #### Analysis Questions 1. **Does the table show a probability distribution? Select all that apply.** - [ ] A. Yes, the table shows a probability distribution. - [ ] B. No, the random variable \( x \) is categorical instead of numerical. - [ ] C. No, the random variable \( x \)'s number values are not associated with probabilities. - [ ] D. No, the sum of all the probabilities is not equal to 1. - [ ] E. No, not every probability is between 0 and 1 inclusive. 2. **Find the mean of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.** - [ ] A. \( \mu = \) ____ child(ren) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. 3. **Find the standard deviation of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.** - [ ] A. \( \sigma = \) ____ child(ren) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. --- #### Graphical Explanation This problem does not include graphs or diagrams. It involves evaluating the provided table to determine if it meets the criteria for a probability distribution, and subsequently calculating the mean and standard deviation. #### Notes for Understanding - A probability distribution
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