Only the part c and d needs to be solved A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with twohoses. 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.p(x, y)X(a) What is P(X = 1 and Y = 1)?P(X= 1 and Y = 1) = 0.20(b) Compute P(X ≤ 1 andXY ≤ 1).P(X ≤ 1 and Y≤ 1) = 0.41Px(x)0(c) Give a word description of the event {X = 0 and Y# 0}.O At most one hose is in use at both islands.O One hose is in use on both islands.O One hose is in use on one island.At least one hose is in use at both islands.yy1 20 0.10 0.05 0.02Compute the probability of this event.P(X 0 and Y# 0) = 0.9XPy(y)1 0.06 0.20 0.082 0.05 0.14 0.30(d) Compute the marginal pmf of X.00Compute the marginal pmf of Y.11Using Px(x), what is P(X ≤ 1)?P(X ≤ 1) =22(e) Are X and Y independent rv's? Explain.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 independent because P(x,y) # Px(x) · Py(y).O X and Y are not independent because P(x,y) = Px(x) Py(Y).

P(X ≤ 1 and Y≤ 1) = 0.41 (c) Give a word description of the event {X = 0 and Y# 0}. At most one hose is in use at both islands. One hose is in use on both islands. One hose is in use on one island. At least one hose is in use at both islands. Compute the probability of this event. P(X + 0 and Y# 0) = 0.9 X (d) Compute the marginal pmf of X. Px(x) 0 у Py(Y) Compute the marginal pmf of Y. 1 0 1 Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = 2 2

P(X ≤ 1 and Y≤ 1) = 0.41 (c) Give a word description of the event {X = 0 and Y# 0}. At most one hose is in use at both islands. One hose is in use on both islands. One hose is in use on one island. At least one hose is in use at both islands. Compute the probability of this event. P(X + 0 and Y# 0) = 0.9 X (d) Compute the marginal pmf of X. Px(x) 0 у Py(Y) Compute the marginal pmf of Y. 1 0 1 Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = 2 2

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.CT: Test

Problem 11CT: aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _

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aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _
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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 of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.05 0.01 1 0.07 0.20 0.08 2 0.05 0.14 0.30 (d) Compute the marginal pmf of X. x 0 1 2 pX(x) Compute the marginal pmf of Y. y 0 1 2 pY(y) Using pX(x), what is P(X ≤ 1)? P(X ≤ 1) =
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