Question 1: Visitors to a Skee-Ball booth attempt to roll a ball into a central target. Define the discrete random variable C: the number of times a customer rolls the ball into the central target in three attempts. The discrete random variable C reflects the customer's score. The PDF of C is as follows: P(C = c) 0.6 c=0 0 1 0.3 c=1 0.15 c=2 0.05 a) Sketch the CDF of C. What proportion of customers roll the ball into the central target at least twice in three attempts? $0 $3.00 $5.00 $7.00 c=3 b) It costs $2.00 to play a single game of Skee-Ball (three attempts) at this booth. Customer winnings (W) are outlined in the table below, alongside the booth's profit (P= W-$2.00) for each possible outcome of the customer's score (C). Customer Score (C) Customer Winnings (W) Booth's Profit (P) +$2.00 -$1.00 2 -$3.00 3 $5.00 Compute E(P), the expected booth's profit for a single game of Skee-Ball. c) How much should the booth charge for a single game of Skee-Ball in order to achieve an expected profit of 40 cents per game? Assume customer winnings amounts remain the same, but the booth's profit (P) will reflect the new price. d) How can the booth achieve an expected profit of 40 cents per game by adjusting customer winnings amounts, while keeping the cost per game equal to $2.00? Note: There is more than one correct answer.
Question 1: Visitors to a Skee-Ball booth attempt to roll a ball into a central target. Define the discrete random variable C: the number of times a customer rolls the ball into the central target in three attempts. The discrete random variable C reflects the customer's score. The PDF of C is as follows: P(C = c) 0.6 c=0 0 1 0.3 c=1 0.15 c=2 0.05 a) Sketch the CDF of C. What proportion of customers roll the ball into the central target at least twice in three attempts? $0 $3.00 $5.00 $7.00 c=3 b) It costs $2.00 to play a single game of Skee-Ball (three attempts) at this booth. Customer winnings (W) are outlined in the table below, alongside the booth's profit (P= W-$2.00) for each possible outcome of the customer's score (C). Customer Score (C) Customer Winnings (W) Booth's Profit (P) +$2.00 -$1.00 2 -$3.00 3 $5.00 Compute E(P), the expected booth's profit for a single game of Skee-Ball. c) How much should the booth charge for a single game of Skee-Ball in order to achieve an expected profit of 40 cents per game? Assume customer winnings amounts remain the same, but the booth's profit (P) will reflect the new price. d) How can the booth achieve an expected profit of 40 cents per game by adjusting customer winnings amounts, while keeping the cost per game equal to $2.00? Note: There is more than one correct answer.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 1: Visitors to a Skee-Ball booth attempt to roll a ball into a central target.
Define the discrete random variable C: the number of times a customer rolls the ball
into the central target in three attempts. The discrete random variable C reflects the
customer's score. The PDF of C is as follows:
P(C = c)
0.5
c=0
0
1
0.3
c=1
0.15
c=2
a) Sketch the CDF of C. What proportion of customers roll the ball into the central target
at least twice in three attempts?
0.05
b) It costs $2.00 to play a single game of Skee-Ball (three attempts) at this booth.
Customer winnings (W) are outlined in the table below, alongside the booth's profit (P =
W-$2.00) for each possible outcome of the customer's score (C).
$0
$3.00
$5.00
$7.00
Customer Score (C) | Customer Winnings (W) Booth's Profit (P)
+$2.00
-$1.00
-$3.00
-$5.00
2
3
Compute E(P), the expected booth's profit for a single game of Skee-Ball.
c) How much should the booth charge for a single game of Skee-Ball in order to achieve
an expected profit of 40 cents per game? Assume customer winnings amounts remain
the same, but the booth's profit (P) will reflect the new price.
d) How can the booth achieve an expected profit of 40 cents per game by adjusting
customer winnings amounts, while keeping the cost per game equal to $2.00?
Note: There is more than one correct answer.
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