Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let X and Y denote the number of cars and buses, respectively, carried on a single trip. The joint pmf of X and Y is given in the table below. *Note that it's readily verified that X and Y are independent. p(x, y)y012x0.0500.0300.020 10.1000.0600.04020.1500.0900.06030.1250.0750.05040.0250.0150.01050.0500.0300.020 (a) Compute the expected value, variance, and standard deviation of the total number of vehicles on a single trip. (Round your standard deviation to two decimal places.) (b) If each car is charged $3 and each bus $10, compute the expected value (in $), variance, and standard deviation (in $) of the revenue resulting from a single trip. (Round your standard deviation to two decimal places.)

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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 53E

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Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let X and Y denote the number of cars and buses, respectively, carried on a single trip. The joint pmf of X and Y is given in the table below. *Note that it's readily verified that X and Y are independent.

p(x, y)	y
0	1	2
x	0.050	0.030	0.020
1	0.100	0.060	0.040
2	0.150	0.090	0.060
3	0.125	0.075	0.050
4	0.025	0.015	0.010
5	0.050	0.030	0.020

(a) Compute the expected value, variance, and standard deviation of the total number of vehicles on a single trip. (Round your standard deviation to two decimal places.)

(b) If each car is charged $3 and each bus $10, compute the expected value (in $), variance, and standard deviation (in $) of the revenue resulting from a single trip. (Round your standard deviation to two decimal places.)

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