**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 \( Y \).\[ f(x, y) = \begin{cases} k(x^2 + y^2), & 0 \leq x \leq 1 \text{ and } 0 \leq y \leq 1 \\0, & \text{otherwise}\end{cases} \]

A box contains 4 tickets with numbers 1, 1, 2, 3.Two tickets will be drawn at random with…

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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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Second Rubber Balls in a Box Setup Stars Stripes Dots Red 8 15 12 Blue 7 3 14 Green 9. 6 Experiment: The rubber balls all have the same size, texture, weight, etc. They cannot be distinguished without looking at them. The rubber balls are mixed around thoroughly in the box. One rubber ball is to be drawn randomly. Let X = the color on the rubber ball. Let Y = the pattern on the rubber ball. 16. Use the Second Rubber Balls in a Box Setup. Find P( NOT Y = Stripes NOT X = Green ). 39 A. 59 45 D. 59 41 В. 59 C. 43 С. 59 *** MORE PROBLEMS ON THE NEXT PAGE. ***

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- 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)