Question

Give the named probability distribution for each of the following random variables with specific parameter values. You should name the parameters, that is, write the parameter name in your answer (for example, Binomial(n=30,p=0.5))

(a) Nia has 6 cats. Each cat has a 25% chance of finishing their dinner. The cats eat independently of each other. What is the distribution of X: the total number of cats that finish their dinner?

(b) Nia has a cat that meows a lot. The meows are independent and she meows on average 2 times per minute. What is the distribution of N: number of times this cat meows in half an hour?

(c) One of Nia’s cat meows when he wants petting. Assuming that the meows are independent of each other and the probability that a meow results in petting is 0.7, what is the distribution of Y: the number of meows until Nia pets him?

(d) There are 30 options of cat toys in a pet store; however, out of those 30, Nia’s cats will only like 4 of them. Nia randomly chooses 2 toys at random and buys them for her cats. What is the distribution of W: the number of toys Nia bought that her cats will like?

Answer 1

Answe a)

As there are six cats and finishing the dinner is the indepedant to each other so itis binomial distribution with total number of is 6 and probabiltiy of 25%

X~Binomial (n =6, p = 0.25)

Answer b)

As the average rate of the meow is the rate of meow in that particular time so it is poisson distribuon:

As it is 2 times per minutes so it will be expected to meow 60 times per half an hour.

Poisson (λ = 60, X =k)

Answer d)

As it binomial distribuion with the total 30 toys she will choose the two toys and with the probability of the like is 0.133 (4/30).

W~Binomial (n =30,p = 0.133)