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- Discrete Probabilities

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Try reviewing these fundamentals first.

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Get Started Now- Lesson: 16:29
- Lesson: 2c4:50
- Lesson: 2d5:48

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

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

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

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

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

- 1.Discrete VS. Continuous
- 2.
**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)Create a probability distribution histogram.b)Using*statistics formulas*to find the mean, variance, and standard deviation of the probability distribution.c)Using*calculator commands*to find the mean, variance, and standard deviation of the probability distribution.d)Based on the “range rule of thumb”, determine the outcomes that are considered as “usual” and “unusual”.

4.

Discrete Probabilities

4.1

Probability distribution - histogram, mean, variance & standard deviation

4.2

Binomial distribution

4.3

Mean and standard deviation of binomial distribution

4.4

Poisson distribution

4.5

Geometric distribution

4.6

Negative binomial distribution

4.7

Hypergeometric distribution

4.8

Properties of expectation