NOTE : It may also be noted that for any value of вЂxвЂ™, the CDF represents a probability. Where F x(x) is called cumulative distribution function (CDF) of a random variable X.ДЇrom equation (2.16), it may be observed that F x(x) is a function of dummy variable вЂxвЂ™ i.e. Now, according to the definition, the cumulative distribution function (CDF) may be written as The probability of this event may be denoted a P (X. Let us consider the probability of the event X. In other words, the comulative distribution function (CDF) provides probabilistic description of a random variable. The Cumulative Distribution Function (CDF) of a random variable вЂXвЂ™ may be defined as the probability that a random variable вЂXвЂ™ takes a value less than or equal to x. Writing the sample space S and values of discrete random variable X asДў.9 CUMULATIVE DISTRIBUTION FUNCTION (CDF) Since, in the given experiment, the random variable X, number of heads, takes only finite values, this is a discrete random variable. Let the random variable, number of heads, be X. Solution: In the three tosses of coins, there are eight possible outcomes. If the number of heads is the random variable, find the probability function for this random variable. In an experiment, three coins are tossed simultaneously. This f(x j) or simply f(x) is called the probability function or probability distribution of the discrete random variable.Д®XAMPLE 2.10.

Let X be a discrete random variable and also let x 1, x 2, x 3, вЂ¦ be the values that X can take. 2.8 PROBABILITY FUNCTION OR PROBABILITY DISTRIBUTION OF A DISCRETE RANDOM VARIABLE

Cdf of discrete random variable