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    Calculating the Mean and Variance of a Poisson Random Variable

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    1. Let X be a random variable with probability density function given by

    f(x) - 2(1 - x), 0 <= x <= 1,
    0, otherwise

    a. Find the density function of Y - X^2
    b. Find the mean and variance of Y.

    2. Let X be a random variable with probability density distribution given by

    f(x) - x, 0 <= x <= 1
    1 < x <= 1.5
    0, otherwise

    Find the probability density function of Y - 10X - 4

    3. Calculate the mean and variance of a Poisson random variable with parameter lambda.

    4. Calculate the mean and variance of a Gamma random variable with parameter alpha and lambda.

    5. Show that the characteristic function of the Cauchy random variable is c^-|w|.

    Find the probability density function of Y - 10X - 4.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:25 am ad1c9bdddf
    https://brainmass.com/statistics/probability/calculating-mean-variance-poisson-random-variable-504514

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