(a) Consider the function f(1) = 1 on 0

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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(a) Consider the function
f(x) :
1
on 0<x <a.
I+1
Find the value of a for which f(r) is a valid pdf.
(b) Let X follow the beta distribution with pdf
S(2) = Kr (1– 2)² on 0 <z< 1.
%3D
Evaluate the value of K.
(c) Let X follow the gamma distribution with pdf
-ba
f(x) =
r(a)
on r>0.
If a = 1 and V(X)=4 find the value of b, and hence find E(X).
%3D
Transcribed Image Text:(a) Consider the function f(x) : 1 on 0<x <a. I+1 Find the value of a for which f(r) is a valid pdf. (b) Let X follow the beta distribution with pdf S(2) = Kr (1– 2)² on 0 <z< 1. %3D Evaluate the value of K. (c) Let X follow the gamma distribution with pdf -ba f(x) = r(a) on r>0. If a = 1 and V(X)=4 find the value of b, and hence find E(X). %3D
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