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

AREA, How do you find the distributive property any faster?

How do you find the distributive property any faster?

Find the length of chord ab, If PA and PB are tangents to a circle from an ...

If PA and PB are tangents to a circle from an outside point P, such that PA=10cm and ∠APB=60 o . Find the length of chord AB.

Fractions, what Is the common denominator for 1/2 and 1/4

what Is the common denominator for 1/2 and 1/4

Determine the fraction of the time, Ipswich has two ambulances. Ambulance 1...

Ipswich has two ambulances. Ambulance 1 is based at the local college and ambulance 2 is based downtown. If a request for an ambulance comes from the local college, the college-bas

Argument, what is the difference between argument and principle argument

what is the difference between argument and principle argument

Determine the range of given algorithm, The division algorithm says that wh...

The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(

Fraction word problems, Alan had 6 books. He read 1/3 of books last week. ...

Alan had 6 books. He read 1/3 of books last week. How many books did Alan read last week?

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