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Consider a sequence of Bernoulli trials with success probability . Trials are contin- ued until the 5th success has occurred, and it is observed that
Consider a sequence of Bernoulli trials with success probability . Trials are contin- ued until the 5th success has occurred, and it is observed that altogether 10 trials are needed. Carry out an exact Likelihood Ratio Test of the null hypothesis H0 : = 3/4. State the distribution of your random variable. You may state and use the MLE of without proof. You will need to use R to get the p-value of your test. Look up the pnbinom() function documen- tation. In your solutions, write down the function call (with argument values) that you used to compute the p-value. Now carry out a Likelihood Ratio Test using the Likelihood Ratio Statistic (LRS). You may use R or distribution tables to compute the p-value here. Do the two tests lead to the same conclusion? You do not need to compute interval estimates for in either test
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