Problem 7. Show the following: (1) Suppose that X and Y are independent random variables. Show that V(X - Y) = V(X) + V(Y). (2) Let X and Y be the number on a ticket in two subsequent draws with replacement from a opaque box with 20 tickets numbered by {1,2,..., 20}. Use Chebyshev's inequality to find a number e such that P(|XY|

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 30E
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Problem 7. Show the following:
(1) Suppose that X and Y are independent random variables. Show that V(X - Y) = V(X) +
V(Y).
(2) Let X and Y be the number on a ticket in two subsequent draws with replacement from a
opaque box with 20 tickets numbered by {1,2,..., 20}. Use Chebyshev's inequality to find a
number e such that
P(|XY| <c) ≥ 0.99.
Transcribed Image Text:Problem 7. Show the following: (1) Suppose that X and Y are independent random variables. Show that V(X - Y) = V(X) + V(Y). (2) Let X and Y be the number on a ticket in two subsequent draws with replacement from a opaque box with 20 tickets numbered by {1,2,..., 20}. Use Chebyshev's inequality to find a number e such that P(|XY| <c) ≥ 0.99.
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