Let Xnnge1 be a sequence of independent random variables such that the probability density function of Xn is given by fn(x) = begincases 1/lambdan e^-x/lambdan & if x ge 0 0 & otherwise, endcases where lambdan = 10 - sumi=1^n 5/2^i-1. Which of the following statements is/are true?

Q52Section ST (Statistics (Q11–Q65))52 of 65

Exponentials with vanishing means

Let $\{X_n\}_{n\ge1}$ be a sequence of independent random variables such that the probability density function of $X_n$ is given by $f_n(x) = \begin{cases} \frac{1}{\lambda_n} e^{-x/\lambda_n} & \text{if } x \ge 0 \ 0 & \text{otherwise,} \end{cases}$ where $\lambda_n = 10 - \sum_{i=1}^{n} \frac{5}{2^{i-1}}$ . Which of the following statements is/are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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