Identify the NAME of the probability mass function and it’s parameters for the f
ID: 3125352 • Letter: I
Question
Identify the NAME of the probability mass function and it’s parameters for the following scenarios:
a. I have 5 keys in my pocket. I come to a door and I know one of the keys will open the door. I select a key at random and try to open the door. If the key doesn’t work, I put it back in my pocket and select another key AT RANDOM. I keep doing this until I finally unlock the door. I am interested in this probability.
b. I flip a coin. I am interested in the probability of getting exactly 7 heads.
c. I am practicing my 3 point shot. I am interested in the probability that it will take me x number of shots to hit ten 3 pointers.
d. I am a popular brand name designer. I have a bolt of fabric from which I want to make a dress. I cut off 2 meters of the fabric and I know that there is on average 6 defects per 400 meters of fabric. I am interested in the probability that the 2 meters of fabric will have at most two defects
Explanation / Answer
a) Geometric distribution with parameter p, p=1/5
f(x) = p q^(x-1) where x is the number of trial to get the success. q=1-p
b) Coin is tosssed until 7th head is not coming. So X ~ geometric(p=1/2)
f(x) = p^7 * q^(x-7)
c) X~binomial(10,1/3)
d) X~Poisson(lambda)