Let Xnnge1 be a sequence of independent random variables such that Xn has Poisson distribution with mean lambdan, where lambdan = lambda + 1/2n, n ge 1, and lambda 0 is an unknown parameter. Which one of the following statements is true?

(B) frac1n sumi=1^n Xi is a consistent estimator of lambda

Q44Section ST (Statistics (Q11–Q65))44 of 65

Consistency of a drifting Poisson average

Let $\{X_n\}_{n\ge1}$ be a sequence of independent random variables such that $X_n$ has Poisson distribution with mean $\lambda_n$ , where $\lambda_n = \lambda + \frac{1}{2n}$ , $n \ge 1$ , and $\lambda > 0$ is an unknown parameter. Which one of the following statements is true?

Pick an option to check your answer. In a mock test a wrong answer here costs 2/3 mark.

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