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Therefore or m = = E (X)

i.e. Mean = E(X) = Expected value.

Also variance (X) = s x2 =

On simplification, we get, the standard deviation,

i.e. s x2 =

Example A business can make a profit of \$2000/- with the probability 0.4 or it can have a loss of \$1000/- with the probability 0.6. What is the expected profit ?

Solution : The discrete random variable ‘x’ is

x1 = \$ 2000 (profit)

x2 = - \$1000 (loss)

With probabilities P1 = 0.4 and P2 = 0.6 respectively

Then expected profit is given by,

E(x) = P1x1 + P2x2

= (0.4) (2000) + (0.6) (-1000)

= \$ 200

Example What is the expected value of the number of points that will be obtained in a single throw of an ordinary dice ?

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Solution : The discrete random variable ‘x’, in this problem assume values

x1 = 1, x2 = 2, x3 = 3, x4 = 4, x5 = 5 and x6 = 6

With probabilities P1 = P2 = P3 = P4 = P5 = P6 = 1/6 (each)

Expected value of the number of points is given by,

E(x) = P1x1 + P2 x2 + P3x3 + P4 x4 + P5 x5 + P6 x6

=

Index

7. 1 Introduction
7.2 Trial
7.3 Sample Space
7. 4 Definition of Probability
7. 5 The Laws of Probability
7. 6 Conditional Probability
7. 7 Theoretical Distribution
7. 8 Binomial Distribution
7. 9 Normal Distribution
Chapter 8