Question

What is a random variable? Why is it important? What is discrete random variable? Continuous random? What is an expected value?

Answer 1

Random varible:

A random variable is defined as the value of the given variable which represents the outcome of a statistical experiment,Suppose X is called the random varible whose possible value are numerical outcomes of random phenomenon

There are many standard probability concepts depend only on the distributions of random variables such as expectations and variances.

There are two type of random varible

a)Discrere random varible:A random varible which takes only countable number of distinct value such as 0,1,2,3,,,,

Example: Number of customer arrived in the telephone booth in a month.

Probabiity Distribution of random varible X for n values defined as P(X=xi)=Pi.

b)Continuous random varible :

A random arible takes infinite number of possible value is called Continuous random varible.

Examle:Weight of person,Height of person

P(x)>=0

and total area under the curve is equal to one

Expeted Value:

Excpected value is mean or average for the probabilty distribution.

For Discreter random varible we define the Excepted value:

where x=1,2,,,,n and P(X)>=0

For Continuos random varible we defind the Expected value is :