7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).

A: 8a. the answer is FALSE.Because failing to reject the null hypothesis does not necessarily mean that...

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A: Step 1: Identify the type of test statistic to useSince both populations are normally distributed...

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: Reference : https://www.omnicalculator.com/statistics/critical-value

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