Homework5

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Author:
erika01
ID:
111831
Filename:
Homework5
Updated:
2011-10-24 17:55:55
Tags:
Kumar CNP
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Description:
Problems and Solutions
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  1. Bernoulli Distribution:

    Parameters: p = prob. of success = (0 ≤ p ≤ 1)
    Range = x {0,1}

    Probability mass function f of this distribution is:
    f(x) = 1-p if x = 0 ; p if x = 1 ; 0 otherwise
    • Mean = p
    • Variance = p (1-p)
  2. Binomial Distribution:

    Notation: B(n,p)
    Parameters: p = 0 < p < 1 (+integer)
    n = numer of trials = n > 0
    Range = x={0,1,...n}

    Probability mass function (pmf) is:
    (n/p) pk (1-p)n-k


    • Mean = np
    • Variance = np (1-p)
  3. Exponential Distribution:

    *x = t ; 1/a = delta

    Parameters: a = (1/x) sacale parameter
    Range = x= {0 ≤ x ≤ ∞}
    Pmf = f(x) = 1/a * e-x/a

    • Mean = delta-1 or 1/delta *delta = λ
    • Variance = delta-2 or (1/delta)2 = (1/λ)2
  4. Geometric Distribution:
    Parameter: p = probability of success = (0 < p < 1)
    Range: x = { 1,2,3…∞}
    Probability mass function (pmf) is:
    f(x) = (1-p)x-1 p
    • Mean = 1/p
    • Variance = (1-p)/ p2
  5. Poisson Distribution:

    Notation: Pois(λ)
    Parameter: λ = mean ; λ >0
    Range: x = {0, 1, 2, 3, …, ∞}
    Probability mass function (pmf) is:

    k / k!) * e

    • Mean = λ
    • Variance = λ

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