Distribution

Question 1

Negative binomial formula

Answer 1

F(x)= c^x-1. (P)^r (1-p)^x-r
r-1

Ev= r/p

Var = 1-p
—-
P

Question 2

Uses of negative binomial distribution

Answer 2

To describe the distribution of parasites

To model random variables
To model contagious discrete events
To model the no of trials before scoring 2,3 goals etc
It can also be employed In tome management

Question 3

Uses of Uniform distribution

Answer 3

Generation of random numbers
Risk analysis
In determining the length of time someone will wait before an event occurs

Question 4

Formula for uniform distribution

Answer 4

1

{. 1/(b-a). ¥ a position

Question 5

Exponential distribution

Answer 5

Used in reliability analysis

Used to measure failure rate of the system

Question 6

E.d formula

Answer 6

F(x)= {1. e^-1/¥x. X_> 0
{/¥
Or €e^€x

E(x)= 1/€. V(x) =1/€^2

Note! ¥ is lamda

Question 7

Normal distribution characteristics

Answer 7

It is bell shaped
It is symmetrical about the mean
Mean=mode=median
It is asymptotic about the x axis

Question 8

Normal distribution formula

Answer 8

1
—- e
¥square root of 2 pie

Question 9

Normal distribution z=

Answer 9

Recall, for the standard normal Variate Z = (X- µ)/σ

Question 10

How to read the z table

For example read 1.78

Answer 10

You’d read 0.8 from the top row
And 1.7 from the vertical row
Dow to the point they meet

Question 11

When f=0.01

Z on the z table=

Answer 11

The value closest to 10000

Which is -1.28