Let X1, X2, … be iid sequence of random variables with common pdf f(x) = begincases e^-x+theta & if x ge theta 0, & if x < theta endcases. If overlineXn = 1/nsumi=1^n Xi, then overlineXn converges in probability to:

Q49Section I (Objective (Q1–Q80))49 of 80

Probability — limit of sample mean for shifted exponential

Let $X_1, X_2, …$ be iid sequence of random variables with common pdf $f(x) = \begin{cases} e^{-x+\theta} & \text{if } x \ge \theta \ 0, & \text{if } x < \theta \end{cases}$ . If $\overline{X_n} = \frac{1}{n}\sum_{i=1}^{n} X_i$ , then $\overline{X_n}$ converges in probability to:

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