Math

ProbabilityQ&A Library12.5. A single observation of a random variable having ageometric distribution is used to test the null hypothesis0 = 0o against the alternative hypothesis 0 = 01 > 09. Ifthe null hypothesis is rejected if and only if the observedvalue of the random variable is greater than or equal tothe positive integer k, find expressions for the probabili-ties of type I and type II errors.%3DvigQuestion

Asked Dec 18, 2019

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Step 1

**Introduction:**

The probability mass function (pmf) and cumulative distribution function (cdf) of a random variable, *X*, having a geometric distribution with parameter, *θ* are as follows:

PMF: *f* (*x*) = (1 – *θ*) *x*–1 *θ*; if *x* = 1, 2, …; *f* (*x*) is 0 , otherwise.

CDF: *F* (*x*) = 1 – (1 – *θ...*

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