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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)=∑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

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Expected value of random variables

  • 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