Suppose the continuous random variable X has probability density func.pdf
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The document discusses a continuous random variable x with a given probability density function. It includes tasks such as finding the probability for a specific interval, as well as calculating the expected value, variance, and cumulative distribution function (CDF). It emphasizes the importance of correctly defining the CDF, particularly noting the lower bound of the support set.
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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