4. a. The density function of a continuous random variable X is given by f(x)= xe* for x>0.Given that:[x²¹e *dx=(n-1)!for ne {1,2,3,...), show that E(X)=2 and Var(X)=2.

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Answered: 4. a. The density function of a…

A First Course in Probability (10th Edition)

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4. a. The density function of a continuous random variable X is given by f(x)= xe* for x>0. Given that: fx-¹e* dx = (n − 1)! for ne {1,2,3,...}, show that E(X)=2 and Var(X) = 2.