Question

Let {Xn}n≥1 be a sequence of independent and identically distributed random variables having the common probability density function
$f(x) = \begin{cases} \frac{2}{x^3}, & x \geq 1 \\\ 0, & \text{otherwise} . \end{cases}$
If $\lim\limits_{n \rightarrow \infin}P(|\frac{1}{n}\sum^n_{i=1}X_i-\theta|< \in)=1$ for all ∈ > 0, then θ equals

• A. 4
• B. 2
• C. ln 4
• D. ln 2

Answer 1

Answer: (B)

2

Answer 2

The correct option is (B) : 2.