**DISCRETE PROBABILITY DISTRIBUTIONS **

**Discrete Random Variables **

**Random Variable** : – represents in number form the possible outcomes, which could occur for some random experiment. Random variables which have a finite number of assigned values are called DISCRETE

**Random Variables ** : A discrete random variable X has a set of distinct possible DISCRETE values.

X= 0, 1 , 2 , 3 , 4 , ……..

For Example:

The number of houses in your neighborhood which have a ‘power safety switch’

The number of new bicycles sold each year by a bicycle store .

The the number of defective light bulbs in the purchase order of a city store.

**A Continuous Random Variable ** X has all possible values in some interval (on a number line.

For Example:

The heights of men could all lie in the interval 50.< x < 250 cm

The volume of water in a rainwater tank during a given month.

NOTE: A discrete random variable involves a count whereas a continuous random variable involves measurement.

**Discrete Probability Distributions **

**Probability Distributions** the set of possible values of a random variable along with the corresponding probabilities. For each random variable there is a probability distribution.

The probability· distribution of a discreet random Variable can be given :

• in table form

in graphical form

in functional form as a probability mass function P(r).

It provides us with all possible value of the variable and the probability of the occurrence of each value.

**Expectation : **Once a probability distribution has been explicitly defined, then this mathematical model of the experiment can be used to further analyze the experiment. One very useful piece of information that may be obtained is the expected value. The EXPECTED VALUE is that quantity that you can expect to obtain when the experiment is performed.

If there are n trials of an experiment and an event has probability p of occurring in each of the trials, then the number of times we expect the event to occur is np.