Discrete distributions

Question 1

Binomial distribution requirements

Answer 1

1) n identical trials
2) two possible outcomes, success or fail
3) probability of success is constant
4) n trials are independent

Question 2

Binomial:
X~Bin( ? )

Answer 2

X~Bin(n,p)

Question 3

E(X) Binomial?

Answer 3

np

Question 4

Var(X) Binomial?

Answer 4

np(1-p)

Question 5

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?

Answer 5

Binomial

Question 6

Geometric:
X~Geo( ? )

Answer 6

X~Geo(p)

Question 7

E(X) Geometric?

Answer 7

1/p

Question 8

Var(X) Geometric?

Answer 8

(1-p)/p^2

Question 9

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.

Answer 9

Geometric

Question 10

Negative Bin
X~Neg( ? )

Answer 10

X~Neg(r,p)

Question 11

E(X) Neg Bin?

Answer 11

r/p

Question 12

Var(X) Neg Bin?

Answer 12

(r(1-p))/p^2

Question 13

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

Answer 13

Negative Binomial

Question 14

HyperGeometric
X~Hyp( ? )

Answer 14

X~Hyp(n,r,m)

Question 15

E(X) HyperGeo?

Answer 15

(mr)/n

Question 16

Var(X) HyperGeo?

Answer 16

(mr(n-r)(n-m))/(n^2(n-1))

Question 17

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

Answer 17

HyperGeo

Question 18

Poisson
X~Poi( ? )

Answer 18

X~Poi(Lambda)

Question 19

E(X) poission?

Answer 19

Lambda

Question 20

Var(X) poisson?

Answer 20

Lambda

Question 21

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.

Answer 21

Poisson