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  3. suppose that the canadian stock market return, den

Suppose that the Canadian stock market return, denoted by a random variable X, varies within {?0.2,...

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Basic Math

  1. Suppose that the Canadian stock market return, denoted by arandom variable X, varies within {?0.2, ?0.1, 0, 0.1, 0.2, 0.4,0.9}, and suppose that P (X = x) = (1 ? x)/10 for x < 0.5 and P(X = 0.9) = 0. Determine each of the following:

    (a) The pdf of X. (b) The cdf of X.

    (c) The expected value of X. (d) The variance of X.

    (e) The standard deviation of X.
    (f) Calculate the sample median of X.

    (g) Let Y denote another random variable such that Y = X2,determine the variance of Y .

  2. Let ?(z) represent the cdf of a N(0,1) random variable at somecut-off point, z. Let X denote

    a N(0.5,1.5) random variable.

    1. (a) Calculate P (?1 ? X ? 2).

    2. (b) Let Y be a N(0,2) random variable that is independent of Xdefined above. Calculate P(?0.5?X+Y ?3).

  3. At the points, x = 0,1,...,6, the cdf for the discrete randomvariable, X, has the value F(x) = x(x + 1)/42. Find the pdf forX.

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