Question: Solve this questions please Question 2: Let X be a continuous random variable with the probability density function (p.d.f.) kxe , f(x) = T E

Solve this questions please

Question 2: Let X be a continuous random variable with the probability density function (p.d.f.) kxe , f(x) = T E [0, 00) otherwise 1. Determine the value of the constant k. 2. Compute the mean E(X). 3. Compute the variance Var(X). 4. Find the moment generating function (m.g.f) of X, and specify the values of t for which it exists. Question 3: Let X be a random variable with the probability density func- tion (p.m.f.) f(x) = x = 1,2, 3, . . . otherwise 1. Determine the value of the constant k. 2. Compute the mean E(X). 3. Compute the variance Var(X). 4. Find the moment generating function (m.g.f) of X, and specify the values of t for which it exists. 5. Use the (m.g.f) to calculate the mean

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