Solution Found!
Nicol (see References) lets the pdf of X be defined by
Chapter 3, Problem 20E(choose chapter or problem)
Nicol (see References) lets the pdf of \(X\) be defined by
\(f(x)= \begin{cases}x, & 0 \leq x \leq 1 \\ c / x^{3}, & 1 \leq x<\infty \\ 0, & \text { elsewhere }\end{cases}\)
Find
(a) The value of \(c\) so that \(f(x)\) is a pdf.
(b) The mean of \(X\) (if it exists).
(c) The variance of \(X\) (if it exists).
(d) \(P(1 / 2 \leq X \leq 2)\).
Equation Transcription:
{
Text Transcription:
X f(x)= { 0, otherwise c/x^3,x 1 x<0 x 1
f(X)
P(½ < or = X < or = 2)
Questions & Answers
QUESTION:
Nicol (see References) lets the pdf of \(X\) be defined by
\(f(x)= \begin{cases}x, & 0 \leq x \leq 1 \\ c / x^{3}, & 1 \leq x<\infty \\ 0, & \text { elsewhere }\end{cases}\)
Find
(a) The value of \(c\) so that \(f(x)\) is a pdf.
(b) The mean of \(X\) (if it exists).
(c) The variance of \(X\) (if it exists).
(d) \(P(1 / 2 \leq X \leq 2)\).
Equation Transcription:
{
Text Transcription:
X f(x)= { 0, otherwise c/x^3,x 1 x<0 x 1
f(X)
P(½ < or = X < or = 2)
ANSWER:
Answer
Step 1 of 5
Total probability =1
f(x)dx=1
+
=1
=1
½-c(0-½)=1
c=1