3.53 Given the joint density function f(z, y) = , 0
A First Course in Probability (10th Edition)
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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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---
**Chapter 3: Random Variables and Probability Distributions**
**3.53** Given the joint density function
\[
f(x, y) =
\begin{cases}
\frac{6 - x - y}{8}, & 0 < x < 2, \, 2 < y < 4 \\
0, & \text{elsewhere}
\end{cases}
\]
find \( P(1 < Y < 3 \mid X = 1.5) \).
---
**3.54** Determine whether the two random variables in Exercise 3.49 are dependent or independent.
---
The problem provides a joint density function for two continuous random variables \( X \) and \( Y \), defined over a specific region. The task is to calculate a conditional probability for \( Y \) given \( X \) has a specific value and to consider the independence of variables in another exercise.
If there were any graphs or diagrams in the image, they would be described in detail here.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F010689eb-d75b-435d-b54f-5b2b21d8dad0%2Fe5d06f96-256d-4af2-8d22-3ee31ed61e57%2Fhtlgcz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here's the transcription suitable for an educational website:
---
**Chapter 3: Random Variables and Probability Distributions**
**3.53** Given the joint density function
\[
f(x, y) =
\begin{cases}
\frac{6 - x - y}{8}, & 0 < x < 2, \, 2 < y < 4 \\
0, & \text{elsewhere}
\end{cases}
\]
find \( P(1 < Y < 3 \mid X = 1.5) \).
---
**3.54** Determine whether the two random variables in Exercise 3.49 are dependent or independent.
---
The problem provides a joint density function for two continuous random variables \( X \) and \( Y \), defined over a specific region. The task is to calculate a conditional probability for \( Y \) given \( X \) has a specific value and to consider the independence of variables in another exercise.
If there were any graphs or diagrams in the image, they would be described in detail here.
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