1 Px(x) = x(x+1) 0, x = 1,2,..., otherwise. F(x) x 1. An alternative method of computing E[X] on defined satisfies the properties of a pmf. Show th ectation does not converge in this case and hence E write 1/x(x + 1) as 1/x − 1/(x+1).] I

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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1. Consider a discrete random variable X with the following pmf:
1
x = 1,2,...,
9
Px(x) =
x(x + 1)
0,
otherwise.
4.2 MOMENTS
F(x)
X
Figure 4.P.1. An alternative method of computing E[X]
Show that the function defined satisfies the properties of a pmf. Show that the
formula (4.1) of expectation does not converge in this case and hence E[X] is
undefined. [Hint: Rewrite 1/x(x + 1) as 1/x - 1/(x+1).]
205
Transcribed Image Text:Problems 1. Consider a discrete random variable X with the following pmf: 1 x = 1,2,..., 9 Px(x) = x(x + 1) 0, otherwise. 4.2 MOMENTS F(x) X Figure 4.P.1. An alternative method of computing E[X] Show that the function defined satisfies the properties of a pmf. Show that the formula (4.1) of expectation does not converge in this case and hence E[X] is undefined. [Hint: Rewrite 1/x(x + 1) as 1/x - 1/(x+1).] 205
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