Probability distribution - histogram, mean, variance & standard deviation

Probability distribution - histogram, mean, variance & standard deviation

Lessons

Notes:
For a probability distribution:
\cdot mean:μ=[xp(x)]mean:\mu = \sum [x \cdot p(x)]
\cdot variance:σ2=[(xμ)2p(x)]=[x2p(x)]μ2variance:\sigma^2 = \sum [(x-\mu)^2 \cdot p(x)]= \sum[x^2 \cdot p(x)] - \mu^2
\cdot standarddeviation:σ=σ2=[(xμ)2p(x)]=[(x2p(x)]μ2standard\;deviation: \sigma = \sqrt{\sigma^2}= \sqrt{\sum [(x-\mu)^2 \cdot p(x)]} = \sqrt{\sum [(x^2 \cdot p(x)]- \mu^2}

Range Rule of Thumb (Usual VS. Unusual):
\cdot maximum usual value =μ+2σ= \mu+2\sigma
\cdot minimum usual value =μ2σ= \mu-2\sigma
  • 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.
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Probability distribution - histogram, mean, variance & standard deviation

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