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.p(x,y)(a) What is P(X= 1 and Y= 1) :0 10 0.10 0.03 0.020.06 0.20 0.070.05 0.14 0.33P(X= 1 and Y= 1) = 0.20(b) Compute P(X ≤ 1 and Y < 1)P(X ≤ 1 and Y≤ 1) =(c) Give a word description of the event { X0 and Y0}.O One hose is in use on one island.O One hose is in use on both islands.O At most one hose is in use at both islands.O At least one hose is in use at both islands.Compute the probability of this event.P(X = 0 and Y # 0) =Py(y)(d) Compute the marginal pmf of X.0Px(x)Compute the marginal pmf of Y.021Using P(x), what is P(X ≤ 1)?P(X ≤1)=[

Given joint pmf p(x,y) of random variables x and y; x: the number of hoses being used on the…

Answered: A service station has both self-service…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.CT: Test

Problem 24CT

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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 0.03 0.02 1 0.07 0.20 0.08 2 0.05 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y—i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.) y 0 1 2 pY|X(y|1) (b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.) y 0 1 2 pY|X(y|2) (d) Given that two hoses are in use at the…
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) =
When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires. (a) If X and Y are independent with pX(0) = 0.5, pX(1) = 0.3, pX(2) = 0.2, and pY(0) = 0.6, pY(1) = 0.1, pY(2) = pY(3) = 0.05, pY(4) = 0.2, display the joint pmf of (X, Y) in a joint probability table. y p(x, y) 0 1 2 3 4 x 0 1 2 (b) Compute P(X ≤ 1 and Y ≤ 1) from the joint probability table.P(X ≤ 1 and Y ≤ 1) = (c) What is P(X + Y = 0) (the probability of no violations)?P(X + Y = 0) =
Find all critical points of the the functionF(x,y)=ln(x2 +y2 +2y+2) in the domain D = {(x,y) ; x2 + y2 < 16}, and decide if each is a local minimum, local maximum or saddle point.
Determine the value of x, y, and z using Gauss-Jordan Reduction Method
Determine the zero(s) of h(x)=−5−5xh(x)=-5-5x.
Use the branch and bound method to find the optimal solution to the IP: max z= 7x1 + 3x2 s.t. 2x1 + x2 <= 9 3x1 + 2x2 <= 13 x1,x2 >= 0; x1,x2 integer
Pt represents price at time t, and Qt represents shares outstanding at time t. Stock A splits three for one in the last period. Stock P0 Q0 P1 Q1 P2 Q2 A 115 600 120 600 40 1,800 B 100 600 95 600 95 600 C 75 700 80 700 80 700 Assuming that the divisor is equal to 3 at time 1, calculate the new divisor at time 2.
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Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

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