Suppose X has the following distribution 1 2|n||n| + 1) P{X = n} = = for n = ±1, ±2,.... (a) What are all medians of X? (b) What is the mean of X? Hint: To get started, compute the following two sums: ΣnP{X = n} and Σ-nP{X = n}. n=1 n=1

Suppose X has the following distribution 1 2|n||n| + 1) P{X = n} = = for n = ±1, ±2,.... (a) What are all medians of X? (b) What is the mean of X? Hint: To get started, compute the following two sums: ΣnP{X = n} and Σ-nP{X = n}. n=1 n=1

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

3. Suppose X has the following distribution
P{X = n} =
2|n||n| + 1)
∞
for n =
(a) What are all medians of X?
(b) What is the mean of X? Hint: To get started, compute the following
two sums:
ΣnP{X = n} and
n=1
∞
= ±1, ±2,....
n=1
-nP{X = n}.

Expert Solution

Step 1

It is given that the PDF of X is:

$P \{X = n\} = \frac{1}{2 |n| (|n| + 1)} f o r n = \pm 1, \pm 2, . . .$

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