Question

Let X be a random variable with the moment generating function
$M(t)=\frac{1}{(1-4t)^5},t \lt\frac{1}{4}.$
Then the lower bounds for P(X < 40), using Chebyshev’s inequality and Markov’s inequality, respectively, are

• A. $\frac{4}{5}$ and $\frac{1}{2}$
• B. $\frac{5}{6}$ and $\frac{1}{2}$
• C. $\frac{4}{5}$ and $\frac{5}{6}$
• D. $\frac{5}{6}$ and $\frac{5}{6}$

Answer 1

Answer: (A)

$\frac{4}{5}$ and $\frac{1}{2}$

Answer 2

The correct option is (A) : $\frac{4}{5}$ and $\frac{1}{2}$.