Question

# Consider a small ferry that can accommodate cars and buses. The toll for cars is \$3,...

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. Suppose the joint distribution of X and Y is as given in the table below.

 y p(x,y) 0 1 2 x 0 0.025 0.015 0.010 1 0.050 0.030 0.020 2 0.105 0.075 0.050 3 0.150 0.090 0.060 4 0.100 0.060 0.040 5 0.050 0.030 0.040

Compute the expected revenue from a single trip. (Round your answer to two decimal places.)
\$

 y p(x,y) 0 1 2 total=P(X) x 0 0.025 0.015 0.01 0.05 1 0.05 0.03 0.02 0.1 2 0.105 0.075 0.05 0.23 3 0.15 0.09 0.06 0.3 4 0.1 0.06 0.04 0.2 5 0.05 0.03 0.04 0.12 total=P(Y) 0.48 0.3 0.22 1
 X P(X) X*P(X) 0 0.050 0.000 1 0.100 0.100 2 0.230 0.460 3 0.300 0.900 4 0.200 0.800 5 0.120 0.600

mean = E[X] = Σx*P(X) =            2.86

=========================

 Y P(Y) Y*P(y) 0 0.480 0.000 1 0.300 0.300 2 0.220 0.440

mean = E[Y] = Σy*P(Y) =            0.74

===================

expected revenue from a single trip = \$3*E(X) + \$10*E(Y) = 3*2.86+10*0.74= \$15.98(answer)

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