# Question: If we let RX t lnMX t show that R X 0

If we let RX(t) = lnMX(t), show that R'X(0) = µ and R''X(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment- generating function

MX(t) = e4(e4 – 1)

MX(t) = e4(e4 – 1)

## Relevant Questions

Show that if a random variable has the probability density f(x) = 1/2 e–|x| for –∞ < x < ∞ Its moment-generating function is given by With reference to Exercise 3.42 on page 90, find the covariance of X and Y. If var(X1) = 5, var(X2) = 4, var(X3) = 7, cov(X1, X2) = 3, cov(X1, X3) = –2, and X2 and X3 are independent, find the covariance of Y1 = X1 – 2X2 + 3X3 and Y2 = –2X1 + 3X2 + 4X3. The probability that Ms. Brown will sell a piece of property at a profit of $ 3,000 is 3/20 , the probability that she will sell it at a profit of $ 1,500 is 7/20 , the probability that she will break even is 7/20 , and the ...With reference to Exercise 3.87 on page 106, find the mean and the variance of the random variable V.Post your question