Question

Let \( X \) be a random variable having the moment generating function

\[ M(t) = \frac{e^t - 1}{t(1 - t)}, \quad t<1. \]

Then

\[ P(X>1) = \underline{\hspace{2cm}} \]

(round off to 2 decimal places).

Hint:

Use the moment generating function to find the distribution of a random variable and then compute the desired probabilities.

Answer 1

Correct Answer: 0.6

To find \( P(X>1) \), we use the moment generating function to first find the probability distribution of \( X \). After calculating the appropriate probabilities, we get: \[ P(X>1) \approx 0.72. \] Thus, the value is \( 0.72 \).