Expected value of Random variables

Statistics and Probability

JANUARY 16, 2017

Submitted by: Afrasiyab Haider

Roll#: 16-ARID-02

FROM: BS-IT 2nd

Submitted to: Ma’am Maryam Ashfaq

1 Expected value of Random variables

Afrasiyab Haider|16-ARID-02

Def: A random variable, X, is a numerical measure of the outcomes of an experiment.

Let X be a random variable assuming the values x1, x2, x3, ... with

corresponding probabilities p(x1), p(x2), p(x3),..... The mean or expected value of X is

defined by E(X) = sum xk p(xk).

symbolized as E(X)Formulas:..

E(X)=∑xipiE(X)=∑xipi

Xi , xi= value of the ith outcomePi , pi = probability of the ith outcome

Example: The staff of the department of mathematics and statistics at university of agriculture Faisalabad reckon that the number of microcomputers getting out of order in a year is well approximated by the following probability distribution

No. out of order: y

0 1 2 3 4

Probability, P(y)

0.3 0.3 0.2 0.1 0.1

Sol:

Expected value= E(Y)= ∑yP(y)

Thus

µ=∑yP(y)= 1.4

y P(y) yP(y)0 0.3 01 0.3 0.32 0.2 0.43 0.1 0.34 0.1 0.4

∑yP(y) 1.4