Expected value, Mathematics

 

Expected Value

For taking decisions under conditions of uncertainty, the concept of expected value of a random variable is used. The expected value is the mean of a probability distribution. The mean is computed as the weighted average of the value that the random variable can assume. The probabilities assigned are used as weights. Thus, it is computed by summing up the random variables multiplied by their respective probabilities of occurrence.

            E[X] = SX P(X)

Example 

 

A person expects a gain of Rs.80, Rs.120, Rs.160 and Rs.20 by investing in a share. The probability distribution of the gains is as follows.

Gain (Rs.)

Probability

80

120

160

20

0.2

0.4

0.3

0.1

The expected gain from the share is,

(80 x 0.2) + (120 x 0.4) + (160 x 0.3) + (20 x 0.1)

=       Rs.(16 + 48 + 48 + 2) = Rs.114

This expected value can be used to compare different investment opportunities. Suppose the investor could invest the amount in another security for which the probability distribution of gains is as follows:

Gain (Rs.)

Probability

150

  80

  20

0.1

0.8

0.1

The expected gain from the second security is,

(150 x 0.1) + (80 x 0.8) + (20 x 0.1)

= Rs.(15 + 64 + 2) = Rs.81

Since the expected gain from the second security is only Rs.81 as compared to Rs.114 from the first, the investor would do well to invest in the first security.

REMARKS

The points to be noted are:

  1. The expected value calculation does not predict the value.

It does not mean that investment in the first security will always lead to a gain of Rs.114 and investment in the second security will always lead to a gain of Rs.81.

  1. Comparing the two expected values and taking a decision based on them only helps in ascertaining which of the alternatives is more likely to lead to higher profits.

Since the expected value of gain from the first security is higher than the expected value of gain from the second, one may conclude that the chance of higher gain is more likely from investing in the first rather than the second.

 

Posted Date: 9/15/2012 1:19:33 AM | Location : United States







Related Discussions:- Expected value, Assignment Help, Ask Question on Expected value, Get Answer, Expert's Help, Expected value Discussions

Write discussion on Expected value
Your posts are moderated
Related Questions
One integer is four times other. The sum of the integers is 5. What is the value of the lesser integer? Let x = the lesser integer and now let y = the greater integer. The ?rst

A closed conical vessel of radius 36 cm and height 60 cm, has some water. When vertex is down then the height of water is 12 cm. What is the height of water when vertex is up?

how is it done

Q. Illustrate Field Properties of Numbers? Ans. What the  associative law of addition  states is this: for any numbers a, b, and c,

How to solve Brahmaguptas Problem? Explain Brahmaguptas Problem solving method?

The horizontal asymptote of (16x+7)(x^2-5)/(x^2+36).

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a)  Determine the p

definition and examples and types

do you have a decimal place value chart

If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans:    AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A