In a car service station, there are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function for (X, Y ) is given by S{(r² + y²), Osx s1;0sy s 1 10, f(x,y) %3D elsewhere. Determine a) the probability that 0.1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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In a car service station, there are two service lines. The random variables X and Y are the
proportions of time that line 1 and line 2 are in use, respectively. The joint probability
density function for (X, Y )
is given by
S((2² + y?), 0sx <1;0sy <1
0,
f(x, y) =
elsewhere.
Determine
a) the probability that 0.1 <X< 0.4 and Y is less than 0.5;
b) Find P(1/4 < X < 1/2 | Y= 3/4).
Transcribed Image Text:In a car service station, there are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function for (X, Y ) is given by S((2² + y?), 0sx <1;0sy <1 0, f(x, y) = elsewhere. Determine a) the probability that 0.1 <X< 0.4 and Y is less than 0.5; b) Find P(1/4 < X < 1/2 | Y= 3/4).
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