How do you calculate the expected value of a random variable?

1 Answer
Nov 1, 2015

E(X) = #sum_0^n x p(x) # where x = 0,1,2,3,... n or #int_0^infty xf(x) dx#


We throw a six faced die is thrown, what is the number than we can expect to see? This question is answered by the mathematical expectation and is denoted by the symbol E(x). As the title says, it is the mathematical expectation. In other words, if the underlying mathematical laws are true, then what value can be expected?
In this, if the mathematical laws are true, then any number from 1 to 6 can turn up and each number has the same probability #(1/6)#. When these values are listed, we have a tabular from where the first column has values 1 to 6 listed and the second column has value #1/6# repeated. Since the mathematical expectation is nothing but the arithmetic mean, we calculate the arithmetic mean here.