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Q40Section B (Section B)40 of 60

Laws of a gamma sum of exponentials

Let X1,X2,…,XnX_{1},X_{2},…,X_{n} be a random sample of size nn (n>1)(n>1) from an Exp⁡(β)\operatorname{Exp}(\beta) distribution, where β>0\beta>0. If T=∑i=1nXiT=\sum_{i=1}^{n}X_{i}, then 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.

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Select every correct option, then submit.