8. The mode for the distribution of random variable X, whether discrete or continuous is the value of x which maximizes the probability mass or density function f for X. Find the mode for the following distributions: 1 (a) f(x) = π(1+x²) 1 O√√2π (c) f(x)=²xe, 0 0. (b) f(x) = -8

8. The mode for the distribution of random variable X, whether discrete or continuous is the value of x which maximizes the probability mass or density function f for X. Find the mode for the following distributions: 1 (a) f(x) = π(1+x²) 1 O√√2π (c) f(x)=²xe, 0 0. (b) f(x) = -8

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

8. The mode for the distribution of random variable X, whether discrete or continuous
is the value of x which maximizes the probability mass or density function f for X.
Find the mode for the following distributions:
1
(a) f(x) =
π(1+x²)'
–84x<0.
1
G√√2
(c) f(x) = 2² xex, 0<x<∞, and zero elsewhere; λ > 0.
(b) f(x) =
-(x - 3)²/20²
e-6
3
-∞0<x<∞0.

Expert Solution

Step 1

Mode find by using first order differentiation of the pdf

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