A random variable X has the moment-generating function of m(t)=e2t+4.5t2. Answer the following questions, 1. Use the derivatives of m(t) to find =E(X). 2. Use the derivatives of m(t) to find 2=var(X). 3. Consider another random variable Y=ex. (a) Use the definition of m(t) to find E(Y). (b) Use m(t) to find var(Y). 4. Identify the distribution [state the parameter values] of X. 5. Compute the probability that X falls between -3 and 0 . 6. Given that X is negative, compute the probability that it is larger than -1 . 7. Compute the probability that Y=eX is at least 1 . A random variable X has the moment-generating function of m(t)=e2t+4.5t2. Answer the following questions, 1. Use the derivatives of m(t) to find =E(X). 2. Use the derivatives of m(t) to find 2=var(X). 3. Consider another random variable Y=ex. (a) Use the definition of m(t) to find E(Y). (b) Use m(t) to find var(Y). 4. Identify the distribution [state the parameter values] of X. 5. Compute the probability that X falls between -3 and 0 . 6. Given that X is negative, compute the probability that it is larger than -1 . 7. Compute the probability that Y=eX is at least 1