Question

1) Define and elaborate upon the following:
(a) A probability density function
(b) A Poisson distribution
(c) A hypergeometric distribution
(d) What does the value of a probability density function denote?

Answer 1

a) Probability density function (PDF) is a function with the following properties:

i) for all values of x

ii)

It is used for a continuous random variable to calculate the probability of a random variable falling within a range of values. Probability is given by the variables

For a continuous random variable probability of the variable taking discrete values is 0. It is continuous over the range of x. Probability is actually the area under the PDF curve.

b) Poisson Distribution

A Poisson random variable is the number of successes that result from a Poisson experiment. The probability distribution of a Poisson random variable is called a Poisson distribution.

eg. X = Number of accidents on a road.

Its PMF is given as;

c)

A hypergeometric experiment is a statistical experiment that has the following properties:

• A sample of size n is randomly selected without replacement from a population of N items.
• In the population, k items can be classified as successes, and N - k items can be classified as failures.

PMF is given by;

n=sample size

N=Population size

M=total number of successes in population.

N-M=total failures

X=Number of successes obtainned in sample

d) Val;ue of probability density function gives the area under the curve for given range. it gives the probability of random variable being in specified range.