Discrete distributions Flashcards
Binomial distribution requirements
1) n identical trials
2) two possible outcomes, success or fail
3) probability of success is constant
4) n trials are independent
Binomial:
X~Bin( ? )
X~Bin(n,p)
E(X) Binomial?
np
Var(X) Binomial?
np(1-p)
Distribution?
A company manufactures fuses, and it is known that 6% of these is defective. A random sample of 10 fuses is
selected for inspection. What is the probability that exactly 8 fuses are manufactured without any defects?
Binomial
Geometric:
X~Geo( ? )
X~Geo(p)
E(X) Geometric?
1/p
Var(X) Geometric?
(1-p)/p^2
Distribution?
A fair die is rolled repeatedly until a number larger than 4 is observed, i.e., until either a 5 or a 6 is observed.
Calculate the probability that the die must be rolled 5 times before a 5 or a 6 is first observed.
Geometric
Negative Bin
X~Neg( ? )
X~Neg(r,p)
E(X) Neg Bin?
r/p
Var(X) Neg Bin?
(r(1-p))/p^2
Distribution?
A fair die is rolled repeatedly and the number of 6’s observed. Calculate the probability that the third 6 occurs on
the seventh roll
Negative Binomial
HyperGeometric
X~Hyp( ? )
X~Hyp(n,r,m)
E(X) HyperGeo?
(mr)/n
Var(X) HyperGeo?
(mr(n-r)(n-m))/(n^2(n-1))
Distribution?
An urn is filled with 10 balls, where 3 are red and 7 are green. In a random sample of 4 balls, what is the probability
that exactly 3 green balls are selected? Let X = number of green balls in the sample of 4
HyperGeo
Poisson
X~Poi( ? )
X~Poi(Lambda)
E(X) poission?
Lambda
Var(X) poisson?
Lambda
Distribution?
A company manufactures rolls of wire. The production process has an average of 3.1 flaws per 1000m length of
wire, according to a Poisson process. Calculate the probability that there are 4 or 5 flaws in a 1000m length of
wire. Let X = number of flaws in a 1000m length of wire.
Poisson
