Definition of random variables, Mathematics

Assignment Help:

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.


Related Discussions:- Definition of random variables

Geometry, Awhat is polygonesk question #Minimum 100 words accepted#

Awhat is polygonesk question #Minimum 100 words accepted#

Binimial, theory behind the greatest term in the binomial expansion

theory behind the greatest term in the binomial expansion

Learning, my math skills are keeping me from getting my ged need help in al...

my math skills are keeping me from getting my ged need help in all areas

How to introduce a child to the symbol for zero, A 'woman was trying to tea...

A 'woman was trying to teach her three-year-old child the numbers from 1to 5 from a children's book on numbers. Each number was illustrated by the same number of trees drawn next t

A graph with a positive slope, A graph with a positive slope shows that the...

A graph with a positive slope shows that the variables depicted on the axes goes in the similar directions.

RECTILINEAR FIGURES, AB,BC,CD ARE THREE CONSECUTIE SIDES OF REGULAR POLYGON...

AB,BC,CD ARE THREE CONSECUTIE SIDES OF REGULAR POLYGON.IF ANGLE BAC IS 18 DEGREE, FIND EXTERIOR ANGLES AND NUMBER OF SIDES ?

Decimals, what is 1/5 + 1/8 equals?

what is 1/5 + 1/8 equals?

Types of series - telescoping series, Telescoping Series  It's now tim...

Telescoping Series  It's now time to look at the telescoping series.  In this section we are going to look at a series that is termed a telescoping series.  The name in this c

Calculate the probability, Calculate the introduction to Probability? P...

Calculate the introduction to Probability? Probability refers to the chance that an event will happen. Probability is presented as the ratio of the number of ways an event can

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd