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).]
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![1. Consider a discrete random variable X with the following pmf:
x = 1, 2,...,
Px (x) =
-{(2+1)
x(x + 1)'
otherwise.
4.2 MOMENTS
F(x)
a
- 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).]
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