(d) Compute the marginal pmf of X.0Px(x)Compute the marginal pmf of Y.yPy(y)11Using px(x), what is P(X < 1)?P(X ≤ 1) = [22(e) Are X and Y independent rv's? Explain.OX and Y are not independent because P(x, y) = Px(x) · Py(y).OX and Y are independent because P(x, y) ‡ px(x) · py(y).OX and Y are independent because P(x, y) = Px(x) - Py(y).OX and Y are not independent because P(x, y) # px(x) · py(y). 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 thenumber of hoses 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)010 0.10 0.05 0.0110.06 0.20 0.072 0.05 0.14 0.32(a) What is P(X= 1 and Y= 1)?P(X= 1 and Y= 1) = ||(b) Compute P(X ≤ 1 and Y ≤ 1).P(X ≤ 1 and Y ≤ 1) = |2(c) Give a word description of the event { X= 0 and Y ‡ 0}.O One hose is in use on one island.O At most one hose is in use at both islands.O One hose is in use on both islands.O At least one hose is in use at both islands.Compute the probability of this event.P(X0 and Y # 0) =

Answered: Image /qna-images/answer/92960899-4bb4-4341-8a1b-6370437bf7cc.jpg

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

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

See similar textbooks