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In: Statistics and Probability

Hummingbirds randomly fly through my back yard at a rate of 5 hummingbirds per hour. Let...

Hummingbirds randomly fly through my back yard at a rate of 5 hummingbirds per hour. Let X = the number of hummingbirds who fly through my backyard during a randomly selected one-hour period. X may be modeled as a Poisson random variable with parameter λ = 5. Let Y equal the total number of hummingbirds who fly through my backyard during a randomly selected two-hour period.

a. For our model, what is expected value of X?
b. What is the probability that X = 4?
c. What is the probability that X < 5?
d. What is the probability that X > 9
e. What is the probability that X = 0
f. Y also has a Poisson distribution. What is the parameter λ for Y?
g. What is variance of Y?
h. What is the standard deviation of Y?
i. What is the probability that Y = 8
j. What is the probability that Y > 8?

Expert Solution

Using

a. For our model, what is expected value of X?

E(X) = 5

b. What is the probability that X = 4?

Using

c. What is the probability that X < 5?

Using

d. What is the probability that X > 9?

Using

e. What is the probability that X = 0

f. Y also has a Poisson distribution. What is the parameter λ for Y?

λ = 2*5 = 10

g. What is variance of Y?

V(Y) = λ = 10

h. What is the standard deviation of Y?

sqrt(λ) = sqrt(10) = 3.1623

i. What is the probability that Y = 8

The provided mean is λ=10.

Using

j. What is the probability that Y > 8?

The provided mean is λ=10.

Using

orchestra answered 1 year ago

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Hummingbirds randomly fly through my back yard at a rate of 5 hummingbirds per hour. Let...

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