For the geometric distribution, show that p(x) = 1 and derive the for F(x). 1.14 expression x=1 Hint: Use the geometric series.
For the geometric distribution, show that p(x) = 1 and derive the for F(x). 1.14 expression x=1 Hint: Use the geometric series.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Please answer question 1.14. Thanks
Transcribed Image Text:Johnsbi bas nsl
1.13 Show that o²= [ (x – µ)² ƒ(x) dx = | x² f(x) dx – µ²
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1.14 For the geometric distribution, show that p(x) = 1 and derive the expression
for F(x).
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x=1
26
ms Hint: Use the geometric series.
1.15 One approach for estimating parameters of a distribution is known as the method of
moments. Consider for example the rectangular distribution where f(x) = 1/(b – a),
a <x< b. By setting the sample mean x (first moment) and sample variance s2 (2nd
moment about the mean) equal to the distribution's mean and variance expressed in
terms of its parameters a and b, the two equations can be solved simultaneously for
their values. Find the method of moments estimators for the rectangular distribution.
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W no
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