Q11.2 A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number ofhoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.yp(x, y)01200.10 0.03 0.0110.07 0.20 0.072 0.06 0.14 0.32 (d) Compute the marginal pmf of X.01Px(x)Compute the marginal pmf of Y.у0Py(y)Using Px(x), what is P(X ≤ 1)?P(X ≤ 1) =(e) Are X and Y independent rv's? Explain.212O X and Y are independent because P(x,y) = Px(x) Py(Y).O X and Y are not independent because P(x,y) = Px(x) · Py(Y).O X and Y are not independent because P(x,y) = Px(x). Py(Y).O X and Y are independent because P(x,y) = Px(x) · Py(Y).

Answered: Image /qna-images/answer/29bb947d-e421-40e4-93ac-ecef972440a8.jpg

(d) Compute the marginal pmf of X. X 0 1 Px(x) Compute the marginal pmf of Y. y Py(Y) Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = (e) Are X and Y independent rv's? Explain. 2 2 O X and Y are independent because P(x,y) = Px(x) Py(Y). O X and Y are not independent because P(x,y) = Px(x) Py(Y). O X and Y are not independent because P(x,y) = Px(x) · Py(Y). O X and Y are independent because P(x,y) = Px(x) Py(Y). 1

(d) Compute the marginal pmf of X. X 0 1 Px(x) Compute the marginal pmf of Y. y Py(Y) Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = (e) Are X and Y independent rv's? Explain. 2 2 O X and Y are independent because P(x,y) = Px(x) Py(Y). O X and Y are not independent because P(x,y) = Px(x) Py(Y). O X and Y are not independent because P(x,y) = Px(x) · Py(Y). O X and Y are independent because P(x,y) = Px(x) Py(Y). 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 51E

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