Definition of random variables, Mathematics

Q. Definition of Random Variables?

Ans.

Up to this point, we have been looking at probabilities of different events. Basically, random variables assign numbers to elements in a sample space. Random variables are understood best if we first look at a few examples and then define the term afterwards.

If a coin is tossed four times, then we can define a random variable X to be the number of heads tossed, so X can be an integer between 0 and 4.

We can define a random variable to be the number of phone calls a company receives in one day. It can take on integer values between 0 and some very large number.

Random variables can take on values other than integers; for example, let X be a random variable representing a person's height.

Definition

A random variable is a variable that assumes a unique numerical value for each of the outcomes in the sample space of a probability experiment.

We normally denote random variables with capital letters (X, Y, etc.) and denote the actual numbers taken by random variables with small letters (x, y, etc.). So if X is the number of cars in the parking lot, then P(X = x) is the probability that there are x cars in the parking lot.

Random variables can be classified into two types:

Discrete random variables take on integer values.

Continuous random variables take values in some interval of real numbers.

Let f(x) = P(X = x). Then f(x) is called the probability function of X. f(x) assigns probabilities to the values of the random variables.

All probability functions have two properties:

 

1066_Random Variables.png

Notice that these properties ensure that for all f(x) ≤ 1 for all x.

Posted Date: 5/3/2013 3:26:35 AM | Location : United States







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