Solution Found!
The number of customers in line at a supermarket express
Chapter 2, Problem 8E(choose chapter or problem)
The number of customers in line at a supermarket express checkout counter is a random variable whose probability mass function is given in the following
table.
For each customer, the number of items to be purchased is a random variable with probability mass function
Let X denote the number of customers in line, and let Y denote the total number of items purchased by all the customers in line. Assume the number of items purchased by one customer is independent of the number of items purchased by any other customer.
a. Find \(P(X=2 \text{ and }Y=2)\).
b. Find \(P(X=2 \text{ and }Y=6)\).
c. Find \(P(Y=2)\).
Equation Transcription:
Text Transcription:
p(x)
p(y)
P(X=2 and Y=2)
P(X=2 and Y=6)
P(Y=2)
Questions & Answers
QUESTION:
The number of customers in line at a supermarket express checkout counter is a random variable whose probability mass function is given in the following
table.
For each customer, the number of items to be purchased is a random variable with probability mass function
Let X denote the number of customers in line, and let Y denote the total number of items purchased by all the customers in line. Assume the number of items purchased by one customer is independent of the number of items purchased by any other customer.
a. Find \(P(X=2 \text{ and }Y=2)\).
b. Find \(P(X=2 \text{ and }Y=6)\).
c. Find \(P(Y=2)\).
Equation Transcription:
Text Transcription:
p(x)
p(y)
P(X=2 and Y=2)
P(X=2 and Y=6)
P(Y=2)
ANSWER:
Answer
Step 1 of 4
Let X denotes no. of customers in line
Let Y denotes total no. of items purchased by all the customers in line
Here they gave probability mass function of X and probability mass function of Y
We have to find the given probabilities
The pmf of X is
X |
0 |
1 |
2 |
3 |
4 |
5 |
P(X) |
0.1 |
0.25 |
0.3 |
0.2 |
0.1 |
0.05 |
The pmf of Y is
Y |
1 |
2 |
3 |
4 |
5 |
6 |
P(Y) |
0.05 |
0.15 |
0.25 |
0.3 |
0.15 |
0.1 |
Write the respective probabilities from the table