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)



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.)










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.)








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.


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
In arithmetic, we deal with numbers. In contrast to this, in algebra, we deal with symbols. These symbols are often represented by lower case alphabets. One of th

how to add a fraction with an uncommon denomoninator

What are the Basic Elements of Reasoning ? There are four basic elements used in geometry. If we say studying geometry is like building a house, then these elements are like d

Binomial Probability Distribution Binomial probability distribution is a set of probabilities for discrete events. Discrete events are those whose outcomes or results can be c

How to Dealing With Exponents on Negative Bases ? Exponents work just the same way on negative bases as they do on positive ones: (-2)0 = 1 Any number (except 0) raised to the

A car was machine washes every car in 5 minutes accurately. It has been calculated that customers will arrive as per to a Poisson distribution at an average of 8 per hour. Calculat

In the previous section we looked at the method of undetermined coefficients for getting a particular solution to p (t) y′′ + q (t) y′ + r (t) y = g (t)    .....................

The probability of a rare disease striking a described population is 0.003. A sample of 10000 was examined. Determine the expected no. suffering from the disease and thus find out

Properties of Logarithms 1. log a xy = log a x + log a y 2.  = log a x - log a y 3. log a x n   = n log