Expected value, Mathematics

Assignment Help:

 

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.

 


Related Discussions:- Expected value

Brownian motion, How do I find the density of a square of a brownian motion...

How do I find the density of a square of a brownian motion .

Example on eulers method, For the initial value problem y' + 2y = 2 - e ...

For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0

Even and odd functions, Even and Odd Functions : This is the final topic ...

Even and Odd Functions : This is the final topic that we have to discuss in this chapter.  Firstly, an even function is any function which satisfies,

Children learn maths from each other, Children Learn From Each Other :  Th...

Children Learn From Each Other :  The other day I had gone to a, nearby school to observe the teacher-children interaction. The children were working on a problem that the teacher

Word problem, A computer is programmed to scan the digits of the counting n...

A computer is programmed to scan the digits of the counting numbers.For example,if it scans 1 2 3 4 5 6 7 8 9 10 11 12 13 then it has scanned 17 digits all together. If the comput

The definition of the derivative, The Definition of the Derivative : In t...

The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the ins

What did she pay per pound, Mona purchased one and a half pounds of turkey ...

Mona purchased one and a half pounds of turkey at the deli for $6.90. What did she pay per pound? Divide the cost of the turkey by the weight; $6.90 ÷ 1.5 = $4.60.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd