Question:

Let {Xn}n≥1 be a sequence of independent and identically distributed random variables having the common probability density function
f(x)={2x3, x1  0,otherwise.f(x) = \begin{cases} \frac{2}{x^3}, &  x \geq 1 \\     0, & \text{otherwise} . \end{cases}
If limnP(1ni=1nXiθ<)=1\lim\limits_{n \rightarrow \infin}P(|\frac{1}{n}\sum^n_{i=1}X_i-\theta|< \in)=1 for all ∈ > 0, then θ equals

Updated On: Oct 1, 2024
  • 4
  • 2
  • ln 4
  • ln 2
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The Correct Option is B

Solution and Explanation

The correct option is (B) : 2.
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