Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area. Let XXX represent the number of customers on a randomly chosen trip. Based on previous data, here is the probability distribution of XXX along with summary statistics: X=\text{\# of customers}X=# of customersX, equals, start text, \#, space, o, f, space, c, u, s, t, o, m, e, r, s, end text 000 111 222 333
P(X)P(X)P, left parenthesis, X, right parenthesis 0.100.100, point, 10 0.200.200, point, 20 0.300.300, point, 30 0.400.400, point, 40
Mean: \mu_X=2μ
X

=2mu, start subscript, X, end subscript, equals, 2
Standard deviation: \sigma_X=1σ
X

=1sigma, start subscript, X, end subscript, equals, 1
Suppose that each trip costs Marcos \$1$1dollar sign, 1 in fuel regardless of how many customers he has, and each customer on a trip pays him \$10$10dollar sign, 10. Let YYY represent Marcos' net gain from a randomly chosen trip.
What are the mean and standard deviation of YYY?
\mu_Y=μ
Y

=mu, start subscript, Y, end subscript, equals
dollars
\sigma_Y=σ
Y

=sigma, start subscript, Y, end subscript, equals
dollars
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