The probability function defined for a discrete random variable is called probability mass function.

Probability mass function and probability density function

A probability function is associated with each value of the random variable. This function is used to compute probabilities for events associated with the random variables. The probability function defined for a discrete random variable is called probability mass function. The probability function associated with continuous random variable is called probability density function.

If, *X* is a discrete random variable taking values *x*1,* x*2* *….* xn *with respective probabilities *p*(*x*1), *p*(*x*2) ….. *p*(*xn*) such that

then p(x) is known as the probability mass function (p.m.f) of the discrete random variable X.

The pair {*xi*, *p*(*xi*); *i* = 1, 2, 3, ... } is known as prabability distribution of *X*.

A coin is tossed two times. If *X* is the number of heads, find the probability mass function of *X*.

Since the coin is tossed two times, the sample space is *S*={*HH*, *HT*, *TH*, *TT*}

If *X* denotes the numbers of heads, the possible values of *X* are 0,1,2 with the following

In example 9.3 the probability mass function of *X* is given in the following table

The above table may be called as the probability distribution function of *X*.

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11th Statistics : Chapter 9 : Random Variables and Mathematical Expectation : Probability Mass Function |

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