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Probability distribution - histogram, mean, variance & standard deviation
- Intro Lesson6:29
- Lesson: 1a4:50
- Lesson: 1b5:48
Probability distribution - histogram, mean, variance & standard deviation
Lessons
For a probability distribution:
⋅ mean:μ=∑[x⋅p(x)]
⋅ variance:σ2=∑[(x−μ)2⋅p(x)]=∑[x2⋅p(x)]−μ2
⋅ standarddeviation:σ=σ2=∑[(x−μ)2⋅p(x)]=∑[(x2⋅p(x)]−μ2
Range Rule of Thumb (Usual VS. Unusual):
⋅ maximum usual value =μ+2σ
⋅ minimum usual value =μ−2σ
⋅ mean:μ=∑[x⋅p(x)]
⋅ variance:σ2=∑[(x−μ)2⋅p(x)]=∑[x2⋅p(x)]−μ2
⋅ standarddeviation:σ=σ2=∑[(x−μ)2⋅p(x)]=∑[(x2⋅p(x)]−μ2
Range Rule of Thumb (Usual VS. Unusual):
⋅ maximum usual value =μ+2σ
⋅ minimum usual value =μ−2σ
- 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".
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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