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    Density function statements

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    True or False (1, 2)
    1. If a continuous random variable X has zero mean, then its density f(x) has to be strictly positive at zero.

    2. If f(x) is a density function on [0,1], then integral 0 to 1 f^2 (x) dx < infinity.

    3. A density function is verbally described as follows: it is zero for x < 1, rises linearly between 1 and 2 to 1/3, remains constant between 2 and 4, decreases linearly to zero from 4 to 5, and remains zero thereafter.
    a) Plot the density function
    b) Find the corresponding CDF and plot it
    c) Find the mean of the distribution
    d) Find P(2.5 < X < 4.5)

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    Problem #1
    Answer: False
    We consider the density function (please see the attached file) with (please see the attached file), then (please see the attached file) and ...

    Solution Summary

    This solution provides a detailed statistics tutorial showing how to plot the given density function, find the corresponding CDF and plotting it, and find the mean of the distribution. It includes completed graphic illustrations.