Expectation and values of variables, probability, definition, example and problem statement

1. 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

2. 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)=∑xipi
E(X)=∑xipi
Xi , xi= value of the ith outcome
Pi , 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 0
1 0.3 0.3
2 0.2 0.4
3 0.1 0.3
4 0.1 0.4
∑yP(y) 1.4