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

Suppose that the Canadian stock market return, denoted by a random 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 .
Let Φ(z) represent the cdf of a N(0,1) random variable at some cut-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 X defined above. Calculate P(−0.5≤X+Y ≤3).
At the points, x = 0,1,...,6, the cdf for the discrete random variable, X, has the value F(x) = x(x + 1)/42. Find the pdf for X.

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Expert Solution

milcah answered 10 months ago

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