A random variable x has a density function f(x) = C*+1), where 0 < x < 2 2 Find: 1. The value of constant c 2. Р(x < 1) 3. Е (X) 4. Е (X?) 5. Var (X)
A random variable x has a density function f(x) = C*+1), where 0 < x < 2 2 Find: 1. The value of constant c 2. Р(x < 1) 3. Е (X) 4. Е (X?) 5. Var (X)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Step 1
"Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To
get the remaining sub-parts solved, please repost the complete question and mention the sub-parts to
be solved.".
Given:
f(x)=c(x+1)2, where 0sxs2
Step 2
1) To find the value constant c
SXERF(x)dx=1c/02x+12dx=1cx24+x202=1c(1+1)=1c=12f(x)=(x+1)4, where Osxs2
2)To find P(xs1)
p(xs1)=/01f(x)dx=S01(x+1)4dx=S01x4+14dx=x28+x401p(x<1)=18+14p(xs1)=38
3) E(x)
E(x)=SxERxf(x)dx=502x(x+1)4dx=S02x24+x4dx=x312+x2802=812+48=1412=76
"Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To
get the remaining sub-parts solved, please repost the complete question and mention the sub-parts to
be solved.".
Transcribed Image Text:A random variable x has a density function
f(x) =
с (х+1)
where 0 <x < 2
2
Find:
1. The value of constant c
2. Р(x < 1)
3. Е(X)
4. Е(X2)
5. Var (X)
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