Question

Let 𝑋 be a random variable having the probability density function
$f(x) =\begin{cases} \frac{5}{x^6}, & \quad \text{if }x>1,\\\ 0, & \quad Otherwise. \end{cases}$
Then, which of the following statements is/are TRUE for the distribution of 𝑋 ?

• A. The coefficient of variation is $\frac{4}{\sqrt15}$
• B. The first quartile is $(\frac{3}{4})^{\frac{1}{5}}$
• C. The median is $(2)^{\frac{1}{5}}$
• D. The upper bound obtained by Chebyshev’s inequality for $p(X≥\frac{5}{2})$ is $\frac{1}{15}$

Answer 1

Answer: (C), (D)

The median is $(2)^{\frac{1}{5}}$

Answer 2

The correct options are: C and D