- A box contains four tickets with numbers 1, 1, 2, 3. Draw two tickets at random with replacement, and let the random variable X be the number in the first ticket, and Y the umber in the second ticket. Calculate cov (X, Y)
- A box contains four tickets with numbers 1, 1, 2, 3. Draw two tickets at random with replacement, and let the random variable X be the number in the first ticket, and Y the umber in the second ticket. Calculate cov (X, Y)
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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![**Question 1:**
A box contains four tickets with numbers 1, 1, 2, 3. Draw two tickets at random with replacement, and let the random variable \( X \) be the number on the first ticket, and \( Y \) the number on the second ticket. Calculate \( \text{cov} (X, Y) \).
**Question 2:**
Using the appropriate value of \( k \), compute the covariance of the random variables \( X \) and \( Y \).
\[
f(x, y) =
\begin{cases}
k(x^2 + y^2), & 0 \leq x \leq 1 \text{ and } 0 \leq y \leq 1 \\
0, & \text{otherwise}
\end{cases}
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Transcribed Image Text:**Question 1:**
A box contains four tickets with numbers 1, 1, 2, 3. Draw two tickets at random with replacement, and let the random variable \( X \) be the number on the first ticket, and \( Y \) the number on the second ticket. Calculate \( \text{cov} (X, Y) \).
**Question 2:**
Using the appropriate value of \( k \), compute the covariance of the random variables \( X \) and \( Y \).
\[
f(x, y) =
\begin{cases}
k(x^2 + y^2), & 0 \leq x \leq 1 \text{ and } 0 \leq y \leq 1 \\
0, & \text{otherwise}
\end{cases}
\]
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