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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".

21.

Discrete Probabilities

21.1

Probability distribution - histogram, mean, variance & standard deviation

21.2

Binomial distribution

21.3

Mean and standard deviation of binomial distribution

21.4

Poisson distribution

21.5

Geometric distribution

21.6

Negative binomial distribution

21.7

Hypergeometric distribution

21.8

Properties of expectation