Expectation

Question 1

Properties of expectation

Answer 1

1. If k is a constant then E(k)=k

Question 2

Hyper geometric distribution

Answer 2

It is a discrete probability distribution that models the selection of n observations without replacements from a finite population of size n where each outcome is either a success or failure

Question 3

Hyper geometric distribution

Answer 3

Mean= nk
—-
N

Variance = N-n. N.k/N
——
N-1
(1-k/N)

PDF= (k/k) (N-k/n-k)
———————
N/n

Question 4

Geometric distribution

Answer 4

The number of trials before the first success in n Bernoulli trials

Question 5

Geometric distribution

Answer 5

F(x) = (1-p)^x-1 p
F(x)= q^x-1 p
Where q+p=1

P= success 
Q= failure 

Mean= 1/p. Expected number of misses
Variance =

Question 6

Uses of geometric distribution

Answer 6

It is used for cost benefit analysis
It is used in sports
In time managemente

Question 7

Poison distribution

Answer 7

It is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if this event occurred with a known average rate and independently of the time since the last event

Question 8

Poisson distribution formula

Answer 8

P(x)= ¥^xE^-¥
————
X!

Question 9

A binomial distribution is

Answer 9

One that has 2 outcomes either you fail or pass

Question 10

We regard p as and q as

Answer 10

Sucess failure
P+q=q
1-p=q

Question 11

Characteristics of binomial

Answer 11

It has n trials each trial results a success or failure

The probability of sucess is constant throughout the experiment

The number of trials are independent

Question 12

Formula for binomial

Answer 12

F(x)= ncx p^x q^n-x

Mean np
Variance npq

Question 13

Negative binomial

Answer 13

Model’s the number of trials before a specified number of sucesses