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- Discrete Probabilities

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Get Started Now- Intro Lesson6:29
- Lesson: 1a4:50
- Lesson: 1b5:48

$\cdot$ $mean:\mu = \sum [x \cdot p(x)]$

$\cdot$ $variance:\sigma^2 = \sum [(x-\mu)^2 \cdot p(x)]= \sum[x^2 \cdot p(x)] - \mu^2$

$\cdot$ $standard\;deviation: \sigma = \sqrt{\sigma^2}= \sqrt{\sum [(x-\mu)^2 \cdot p(x)]} = \sqrt{\sum [(x^2 \cdot p(x)]- \mu^2}$

$\cdot$ maximum usual value $= \mu+2\sigma$

$\cdot$ minimum usual value $= \mu-2\sigma$

- IntroductionDiscrete VS. Continuous
- 1.
**Probability Histogram, Mean, Variance and Standard Deviation**

The following table gives the probability distribution of a loaded (weighted) die:

**outcome****probability**1

0.05

2

0.10

3

0.30

4

0.33

5

0.15

6

0.07

a)Using*calculator commands*to find the mean, variance, and standard deviation of the probability distribution.b)Based on the "range rule of thumb", determine the outcomes that are considered as "usual" and "unusual".