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Suppose the continuous random variable X has probability density function f(x) = x^2/3 for -2
LT xLT 1, 0 else where. Find P{-2 LTX LT -1). Find E(X). Find V(X). Find the cumulative
distribution function (cdf) of X, F(x). Be sure to define the cdf for all x (-infinity, infinity).
Show F(x) using clear notation. The most common mistake for the cdf is forgetting the lower
bound of the support set, which is -2 here.
Solution

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Suppose the continuous random variable X has probability density func.pdf

  • 1. Suppose the continuous random variable X has probability density function f(x) = x^2/3 for -2 LT xLT 1, 0 else where. Find P{-2 LTX LT -1). Find E(X). Find V(X). Find the cumulative distribution function (cdf) of X, F(x). Be sure to define the cdf for all x (-infinity, infinity). Show F(x) using clear notation. The most common mistake for the cdf is forgetting the lower bound of the support set, which is -2 here. Solution