Match the descriptions below to the most appropriate of the six families of dist

Question

Match the descriptions below to the most appropriate of the six families of distributions.

Binomial, Hypergeometric, Gamma, Poisson, Negative binomial, Normal

(a) Let X = the total weight of the 400 pieces of kibble that I fed Peter for breakfast this morning.

(b) There are 4 squeak toys and 3 rope toys Peter’s toy bin. Peter reaches in and grabs 3 toys at random (that’s how many he can fit in his mouth at once). Let X = the number of squeak toys that end up in his mouth.

(c) Peter sits on by a bench downtown and, independently, decides to lick (with probability p) or not lick (with probability 1 p) the people who pass by. Let X = the number of people who walk buy until the third one to get licked.

(d) Out of the next 20 people who pass by on the sidewalk, let X = the number of them that get licked.

(e) When I buy a new bag of dog kibble, I pour it from the bag into a plastic storage bin. Each piece has some small probability (independently) of bouncing out of the bin and onto the floor (and hence immediately being eaten). Let X = the number of pieces of kibble that Peter gets to eat while I’m pouring it into the bin.

(f) Once I start pouring the kibble, let X = the length of time that will elapse until five pieces of kibble find their way onto the floor and into Peter’s belly.

Explanation / Answer

a) The Normal Distribution.

X = the total weight of the 400 pieces of kibble that I fed Peter for breakfast this morning. Since the weight can take any random value on contnuous scale. This is a case of Normal Distribution.

b) Hypergeometric

This example is a case of hypergeometric distribution since we are selecting a perticular type of sample when population is divided into two group.

c) Negative Binomial

This is the case of Negative binomial distribution. As X is the random variable that the number of people who walk untill getting 3rd success.

d) Binomial Distribution

This is a case of binomial with probability p.

e) Poisson Distribution.

Since each of piece have small probability of bouncing out from the bag that means the bouncing oocurs at some independent interval. hence this is a situation of Poisson.

f) Gamma Distribution:

In this case the peter have to wait upto 5th success. Waiting time upto kth success follows gamma distribution.

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