Problem 8: Consider the density function f(x) = a) Evaluate k. b) Find F(x). c) Use F(x) to evaluate P(2 < X < 3). k X4' 0, x > 1, x ≤ 1
Problem 8: Consider the density function f(x) = a) Evaluate k. b) Find F(x). c) Use F(x) to evaluate P(2 < X < 3). k X4' 0, x > 1, x ≤ 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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![**Problem 8:**
Consider the density function
\[
f(x) =
\begin{cases}
\frac{k}{x^4}, & x > 1, \\
0, & x \leq 1
\end{cases}
\]
a) Evaluate \( k \).
b) Find \( F(x) \).
c) Use \( F(x) \) to evaluate \( P(2 < X < 3) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b3f294e-d3c8-4475-8e8e-f2b525027412%2F81858d28-a4da-48b7-831a-b149b401e3cf%2Fuk9nged_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 8:**
Consider the density function
\[
f(x) =
\begin{cases}
\frac{k}{x^4}, & x > 1, \\
0, & x \leq 1
\end{cases}
\]
a) Evaluate \( k \).
b) Find \( F(x) \).
c) Use \( F(x) \) to evaluate \( P(2 < X < 3) \).
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