MATLAB: An Introduction with Applications
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Publisher: John Wiley & Sons Inc
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Transcribed Image Text:**Probability Distribution of Dogs per Household**
The following details a probability distribution for the number of dogs per household in a small town:
| Dogs | Probability |
|------|-------------|
| 0 | 0.622 |
| 1 | 0.236 |
| 2 | 0.094 |
| 3 | 0.026 |
| 4 | 0.014 |
| 5 | 0.008 |
**Tasks:**
(a) *Calculate the Mean, Variance, and Standard Deviation of the Probability Distribution.*
- **Mean (μ):** Compute the expected value by multiplying each number of dogs by its probability and summing the results.
\(\mu = \sum (x \cdot P(x))\)
\(\mu = \boxed{\ } \) (Round to one decimal place as needed.)
- **Variance (\(\sigma^2\)):** Compute the variance by finding the expected value of the squared deviations from the mean.
\(\sigma^2 = \sum ((x - \mu)^2 \cdot P(x))\)
\(\sigma^2 = \boxed{\ } \) (Round to one decimal place as needed.)
- **Standard Deviation (\(\sigma\)):** The standard deviation is the square root of the variance.
\(\sigma = \boxed{\ } \) (Round to one decimal place as needed.)
*Click to select your answer(s).*
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