**4. Probability distributions**

A probability distribution is a function that describes the probability of obtaining the possible values that a random variable may assume. In other words, the variable values differ depending on the distribution of the underlying probability. In Statistics, the probability distribution gives the possibility of each outcome of a random experiment or occurrences [5].

Suppose you take a random sample and measure the weight of the subjects. You will establish a distribution of weights when you calculate weights. This form of distribution is useful when you need to know the outcomes are most likely to occur, the spread of possible values, and the probability of various outcomes [6].

The probability distributions suggest the probability of an occurrence or result. Statistics use the following notation to define the probabilities:

*P X*ð Þ¼ the probability that the random variable will have a particular value of *X:*

A probability model needs a measure of the probability, typically written to P. This probability measure must allocate a probability to each case A, a probability P(A).

We require the following properties:

1.P(X) is always a nonnegative real number, between 0 and 1 inclusive.

2.P (Ø) = 0, i.e., if X is the empty set Ø, then P(X) = 0.

3.P(S) = 1, i.e., if X is the entire sample space S, then P(X) = 1.

4.P is (countably) additive, meaning that if X1, X2,... is a finite or countable sequence of disjoint events, then P(X1 ∪ X2 ∪���) = P(X1) + P(X2) + ——.
