Introduction for finding Expected Value:
In probability theory and statistics, the expected value (or expectation value, or mathematical expectation, or mean, or first moment) of a random variable is the integral of the random variable with respect to its probability measure.For discrete random variables this is equivalent to the probability-weighted sum of the possible values.For continuous random variables with a density function it is the probability density-weighted integral of the possible values. I like to share this Expected Value of Random Variable with you all through my article.
Find the expected value (EV):
The calculated value of a variable quantity which is most likely to occur. If a variable x can take any of the values (x1,x2,…..,xn) with corresponding probabilities (p1,p2,.......,pn) then expected value x or expectation of x is written as E(x)=p1x1+p2x2+…….+pnxn.
The general format to find the Expected value is
To find theExpected Value = Number of offspring x Respective Probability.
Example 1:
Tossing a coin twice times. Let X denotes the number of heads which appear. Then the possible values of x are 0, 1, 2 and 3. The corresponding probabilities are 1/8, 3/8, and 3/8.Thus, the expected value of x equals
X=0(1/8) +1(3/8) +2(1/8) =5/8
This section we shall see a faster method to compute this expected value, based on the information that x can be written as a sum of simple random variables.
Examples how to find the expected value
The drink and fire detector is doing well, the Expected Value is the profit multiplied by its probability, 900,000 x 0.5 = 450,000.
If the fire detector project fails is (-10,000) x 0.5 = (-5,000).
The decision to develop the drink and fire detector is the sum of the Expected Value for all the eventualities.
Chance node to find expected value = success + failure = 450,000 + (-5,000) = 500,000.
Similarly, the Expected Value for the decision to develop the motion detector is given by
Expected Value = (390,000 x 0.8) + [(-10,000) x 0.2] = 310,000.
Following Project Expected value (EV) is the sum of all the combined payoffs and probabilities for each node.
The drink and fire Project of expected value:
Node `rArr` 1.Drink & fire detector (-100,000) `rArr` 1. (0.5) Success (900,000)
EV=400,000
`rArr` 2. (0.5) Failure (-100,000)
`rArr` 2.Motion Detector (-10,000) `rArr` 1. (0.8) Success (390,000
EV=400,000
`rArr` 2. (0.2) Failure (-10,000)
EV = 0
`rArr` 3.Neither (0)
Where EV `|->` Expected value
Expected Value Calculation - Expected Value
= (900,000 x 0.5) + [(-100,000) x 0.5] = 400,000
The drink and fire detector project has a higher EV than the motion detector. You can report the study with these summarized presentation points:
The drink and fire detector is the better project to develop, despite the greater risk. The significantly bigger anticipated profits make the risk more acceptable than the competing project.
In probability theory and statistics, the expected value (or expectation value, or mathematical expectation, or mean, or first moment) of a random variable is the integral of the random variable with respect to its probability measure.For discrete random variables this is equivalent to the probability-weighted sum of the possible values.For continuous random variables with a density function it is the probability density-weighted integral of the possible values. I like to share this Expected Value of Random Variable with you all through my article.
Find the expected value (EV):
The calculated value of a variable quantity which is most likely to occur. If a variable x can take any of the values (x1,x2,…..,xn) with corresponding probabilities (p1,p2,.......,pn) then expected value x or expectation of x is written as E(x)=p1x1+p2x2+…….+pnxn.
The general format to find the Expected value is
To find theExpected Value = Number of offspring x Respective Probability.
Example 1:
Tossing a coin twice times. Let X denotes the number of heads which appear. Then the possible values of x are 0, 1, 2 and 3. The corresponding probabilities are 1/8, 3/8, and 3/8.Thus, the expected value of x equals
X=0(1/8) +1(3/8) +2(1/8) =5/8
This section we shall see a faster method to compute this expected value, based on the information that x can be written as a sum of simple random variables.
Examples how to find the expected value
The drink and fire detector is doing well, the Expected Value is the profit multiplied by its probability, 900,000 x 0.5 = 450,000.
If the fire detector project fails is (-10,000) x 0.5 = (-5,000).
The decision to develop the drink and fire detector is the sum of the Expected Value for all the eventualities.
Chance node to find expected value = success + failure = 450,000 + (-5,000) = 500,000.
Similarly, the Expected Value for the decision to develop the motion detector is given by
Expected Value = (390,000 x 0.8) + [(-10,000) x 0.2] = 310,000.
Following Project Expected value (EV) is the sum of all the combined payoffs and probabilities for each node.
The drink and fire Project of expected value:
Node `rArr` 1.Drink & fire detector (-100,000) `rArr` 1. (0.5) Success (900,000)
EV=400,000
`rArr` 2. (0.5) Failure (-100,000)
`rArr` 2.Motion Detector (-10,000) `rArr` 1. (0.8) Success (390,000
EV=400,000
`rArr` 2. (0.2) Failure (-10,000)
EV = 0
`rArr` 3.Neither (0)
Where EV `|->` Expected value
Expected Value Calculation - Expected Value
= (900,000 x 0.5) + [(-100,000) x 0.5] = 400,000
The drink and fire detector project has a higher EV than the motion detector. You can report the study with these summarized presentation points:
The drink and fire detector is the better project to develop, despite the greater risk. The significantly bigger anticipated profits make the risk more acceptable than the competing project.
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