As soon as possible! Let X and Y be continuous random variables with joint PDF Find:fx,x(x, y) = { cay² 0≤x≤ 1,0 ≤8≤1otherwisea) Constant c.b) P[X > Y], P[Y < X²].c) P[min(X,Y) ≤ 1/2], P[max(X,Y) < 3/4].d) Find the marginal PDFs fx(x) and fy(y).e) Are these random variables independent?

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Answered: Find: fx,x(x, y) = { cay² 0≤x≤ 1,0 ≤8≤1…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 33E

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As soon as possible!

Let X and Y be continuous random variables with joint PDF

Find:
fx,x(x, y) = { cay² 0≤x≤ 1,0 ≤8≤1
otherwise
a) Constant c.
b) P[X > Y], P[Y < X²].
c) P[min(X,Y) ≤ 1/2], P[max(X,Y) < 3/4].
d) Find the marginal PDFs fx(x) and fy(y).
e) Are these random variables independent?

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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