Random variables X and Y have the joint PMF (a) What is the value of the constant

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Random variables X and Y have the joint PMF

(a) What is the value of the constant c?

(b) What is P(Y < X)?

(d) What is P(Y = X)?

(e) What is P(Y = 3)?

(f) Find the marginal PMFs pX(x) and pY (y).

(g) Find the expectations E[X], E[Y] and E[XY].

(h) Find the variances var(X), var(Y) and var(X + Y).

(i) Let A denote the event X ≥ Y. Find E[X | A] and var(X | A).

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Statistics for Business Decision Making and Analysis

ISBN: 978-0321890269

2nd edition

Authors: Robert Stine, Dean Foster

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Posted Date: Apr 07, 2020 11:50 PM

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Random variables X and Y have the joint PMF (a) What is the value of the constant

Question:

c(x² + y²), if x E {1,2, 4} and y E {1,3}, 0, otherwise. PX,y(x, y) c(x² + y²), if x E {1,2, 4} and y E {1,3}, 0, otherwise. PX,y(x, y)

Expert Answer:

a From the joint PMF there are six x y coordinate pairs with nonzero probabilities of occurring These pairs are 11 13 21 23 41 and 43 The probability ... View the full answer

Statistics for Business Decision Making and Analysis

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