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# Consider the manufacture of Grandmotherâ€™sFudge Nut Butter Cookies. Grandmother has noted that the number of nuts in acookie is a random variable with a Poisson mass function and that the average...

Consider the manufacture of Grandmotherâ€™sFudge Nut Butter Cookies. Grandmother has noted that the number of nuts in acookie is a random variable with a Poisson mass function and that the average number ofnuts per cookie is 1.5.
a. What is the numerical value of the probability of having at least one nut in a randomlyselected cookie?
b. Determine the numerical value of the variance of the number of nuts per cookie.
c. Determine the probability that a box of exactly M cookies contains exactly the expected value of the number of nuts for a box of N cookies. (M = 1, 2, Â· Â· Â· ;N = 1, 2, Â· Â· Â·). Hint:semantics here are very important. You need to consider different cases of M and N,even and odd and realize that nuts are always whole. Just do some examples and then generalize.
d. What is the probability that a nut selected at random goes into a cookie containing exactly K nuts? Hint: a nut must go into a cookie and so this distribution can not contain zero nuts. Therefore, a suitable normalization of the original Poisson is needed.

Answered Same Day Dec 25, 2021

## Solution

Robert answered on Dec 25 2021
1
The average number of nuts per cookies =1.5
Poisson distribution P(x; =
Where,
Actual number of success
The average number of successes with in a given range
Here,
E(x) =
V(x) =
a) The numeric value of probability of having t least one nut in random selected cookie is
computed below
=
=
=
=
) The numerical value of the variance of the number of nuts per cookie ...
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