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Q19Section I (Objective (Q1–Q80))19 of 80

Statistical Inference — SPRT no-decision probability for exponential mean

Let X1,X2,X3,…,XnX_1, X_2, X_3, …, X_n be a sequence of iid observations from an exponential distribution with mean 1θ\frac{1}{\theta}, θ>0\theta > 0. To test H0:θ=1H_0 : \theta = 1 versus H1:θ=2H_1 : \theta = 2, SPRT is used. What is the probability that the procedure has no decision at the first stage when α=β=0.1\alpha = \beta = 0.1 and H0H_0 is true?

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