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Asked Dec 18, 2019
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12.5. A single observation of a random variable having a
geometric distribution is used to test the null hypothesis
0 = 0o against the alternative hypothesis 0 = 01 > 09. If
the null hypothesis is rejected if and only if the observed
value of the random variable is greater than or equal to
the positive integer k, find expressions for the probabili-
ties of type I and type II errors.
%3D
vig
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12.5. A single observation of a random variable having a geometric distribution is used to test the null hypothesis 0 = 0o against the alternative hypothesis 0 = 01 > 09. If the null hypothesis is rejected if and only if the observed value of the random variable is greater than or equal to the positive integer k, find expressions for the probabili- ties of type I and type II errors. %3D vig

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Expert Answer

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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