There are two food carts serving food at a local park. At any given time, Let A denote the number of customers in line at Food Cart A, and let B denote the number of customers in line at Foo Cart B. The joint PMF of A and B is as given in the following table. 1 2 3 A
There are two food carts serving food at a local park. At any given time, Let A denote the number of customers in line at Food Cart A, and let B denote the number of customers in line at Foo Cart B. The joint PMF of A and B is as given in the following table. 1 2 3 A
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:3. There are two food carts serving food at a local park. At any given time, Let A denote the number
of customers in line at Food Cart A, and let B denote the number of customers in line at Food
Cart B. The joint PMF of A and B is as given in the following table.
В
1
2
A
0.09
0.05
0.03
1
0.01
0.01
0.05
0.04
2
0.08
0.06
0.1
0.07
3
0.03
0.01
0.1
4
0.01
0.15
0.05
0.06
a. What is P(A = B), that is, the probability that the numbers of customers in the two lines
are identical?
b. What is the probability that the total number of customers in the two lines is exactly four?
At least four?
c. Determine the marginal PMF of A and B and then calculate the expected number of
customers in line at Food Cart B.
d. If at a given time there are 3 customers in line at Food cart A, what is the probability of 2
customers being in line at Food Cart B?
e. Are A and B independent random variables? Explain.
Transcribed Image Text:7. The mode and variance of the daily income of 2000 workers are Tk. 100 and Tk? 36 respectively.
The income of workers are distributed normally.
a. Find the expected number of workers whose daily income are
i. between Tk. 100 and Tk. 105
ii. greater than Tk. 110
iii. less than Tk. 90
iv. less than Tk. 90 or greater than Tk. 107
b. Determine the 85th percentile value for the daily income of the 2000 workers.
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