Question: Let X be a continuous random variable with density when x > 0, elsewhere. 3e-3x 0, (a) Verify that f is a density function.

Let X be a continuous random variable with density when x > 0, elsewhere. 3e-3x 0, (a) Verify that f is a density function. (b) Calculate P(-1 < X < 1). (c) Calculate P(X < 5). (d) Calculate P(2 < X < 4 | X < 5). f(x) = = 2 (e) Find the cumulative distribution function of X. (f) Find the mean of X. Compute E(ex). (g) Find the variance of X.

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