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
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
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 1E: If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the...
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac78b595-c111-4964-a356-c58c592fa84c%2Ff4465469-8605-4377-85c7-f243edf828cf%2Fmha1j1j_processed.jpeg&w=3840&q=75)
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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