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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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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