What is P(Y = 15)? If the rate of orders falls to 2.1 per minute: b. What is P(X = 1)? c. What is the variance for X?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A company's marketing department claims that the number of orders that are placed using their
e-commerce store has a Poisson distribution with mean of 3.5 orders per minute. Let X be the number of
orders in 1 minute. Let Y be the number of orders in 5 minutes. If the claim of a mean of 3.5 orders per
minute is true

a. What is P(Y = 15)?

If the rate of orders falls to 2.1 per minute:

b. What is P(X = 1)?

c. What is the variance for X?

 

Expert Solution
Step 1

It is given that

X follows Poisson with parameter = 3.5.

Also, 

Y denotes the number of order in 5 minutes then 

Y follows Poisson with parameter = 5 × 3.5 = 17.5

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