Question

In: Statistics and Probability

A healthy female dog that is not being raised by breeders typically produces an average of...

A healthy female dog that is not being raised by breeders typically produces an average of two litters per year. Suppose that one healthy female dog is randomly chosen.

In words, define the random variable X.
List the values that X may take on.
Give the distribution of X. X ~ _______
Find the probability that she has no litters in one year.
Find the probability that she has at least one litter in one year.
Find the probability that she has exactly four litters in one year.

Expert Solution

A healthy female dog that is not being raised by breeders typically produces an average of two litters per year. Suppose that one healthy female dog is randomly chosen.

a) In words, define the random variable X.

ans: X can be defined as the number litters per year produced by a randomly chosen healthy female dog

b) List the values that X may take on.

The number of litters may be 0,1,2, and so on to a large number (theoretically)

ans: X can take 0,1,2,...

c) Give the distribution of X.

We know that a healthy female dog that is not being raised by breeders typically produces an average of two litters per year. We can say that X has a Poisson distribution with mean =2 and parameter

ans:

The probability that a randomly selected healthy female dog has X=x litter in one year is

d) the probability that she has no litters in one year is

ans: the probability that she has no litters in one year is 0.1353

e) the probability that she has at least one litter (which is one or more ) in one year is

ans: the probability that she has at least one litter in one year is 0.8647

f) the probability that she has exactly four litters in one year is

ans: the probability that she has exactly four litters in one year is 0.0902

orchestra answered 1 year ago

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