In a car service station, there are two service lines. The random variables X and Y are theproportions of time that line 1 and line 2 are in use, respectively. The joint probabilitydensity function for (X, Y ) is given byS{(r² + y²), 0sx <1;0sy s1[0,f(x, y) =elsewhere.Determinea) whether or not X and Y are independent.b) the marginal distribution of X;c) the marginal distribution of Y;d) the probability that 0.1

a. The given joint pdf is f(x,y)=32(x2+y2) 0≤x≤1, 0≤y≤1 f(x,y)=g(x)h(y) g and h…

Answered: Determine a) whether or not X and Y are…

Determine a) whether or not X and Y are independent. b) the marginal distribution of X; c) the marginal distribution of Y;

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

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Question

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), 0sx <1;0sy s1
[0,
f(x, y) =
elsewhere.
Determine
a) whether or not X and Y are independent.
b) the marginal distribution of X;
c) the marginal distribution of Y;
d) the probability that 0.1 <X<0.4 and Y is less than 0.5;
e) Find P(1/4 < X < 1/2 ] Y= 3/4).

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