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







Related Discussions:- Definition of random variables, Assignment Help, Ask Question on Definition of random variables, Get Answer, Expert's Help, Definition of random variables Discussions

Write discussion on Definition of random variables
Your posts are moderated
Related Questions
Samantha owns a rectangular field that has an area of 3,280 square feet. The length of the field is 2 more than twice the width. What is the width of the field? Let w = the wid

Compute the linear convolution of the discrete-time signal x(n) ={3, 2, 2,1} and the impulse response function of a filter h(n) = {2, 1, 3} using the DFT and the IDFT.

Negative four is multiplied through the quantity x + 8. If 6x is then added to this, the output is 2x + 32. What is the value of x? twice the quantity x + 6 is divided by negative

one bathroom is 0.3m long how long is a row of 8 tiles

three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.

Value of perfect information This relates to the amount that we would pay for an item of information such would enable us to forecast the exact conditions of the market and act

1/a+b+x  =1/a+1/b+1/x    a+b ≠ 0 Ans: 1/a+b+x  =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒  x - ( a + b + x )/ x ( a + b + x )   = + a + b/ ab ⇒

explain the characteristics of statistics

find any integer from 1-128 on a logarithmic scale

Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of