subject: Positive Expected Value [print this page] Introduction to positive expected value: Introduction to positive expected value:
The positive learning in the field of probability is used to justify the distribution of a random variable in a special case. The positive expected value is accepted by the laws of large numbers. The expected value is obtained for the sample of a data. It leads up to infinity. In positive expected value article, you can learn about its properties and example of expected value.
Properties of Positive Expected Value:
The following are the properties of positive expected value. These are the factors that determine the positive expected value.
The sum of the expexted value of the experiment is equal to the individual expected values.
E(X + Y) = E(X) + E(Y).
The expected value multiplied with a constant is equal to the constant multiplied with the expected value.
E (cX) = cE(X).
If the probability function is zero, then the expected value is also zero.
if X = 0 then E(X) = 0.
The product of probability function is equal to the product of expected value.
if X Y then E(X) E(Y)
The modulus taken to the expected value variable is equal to the modulus of expected value.
|E(X)| E (|X|)
The above properties justify the solution of positive expected value.
Applications positive expected value:
The positive expected value is used to identify the distribution of a random variable.
The positive expected value determines the probability of a random experiment.
The positive value plays a key role in the field of probability.
It is one of the essential factors of probability functions.
These are the applications of positive expected value.
Positive Expected Value Solved Example:
A fair coin is tossed three times. While the experiment let Y is the number of heads obtained. The conditional probability values of the experiment is given by 1/4, 3/4, 3/4 and 1/4. Then find the expected value of the experiment.
Solution:
The expected value of the experiment is obtained from the formula,
E(Y) = ? (m(y)) with the lower limit of y e O
Putting the known values from the experiment in the above formula,
= 0(1/4) + 1(3/4) + 2(3/4) + 3(1/4)
= 0 + 3/4 +3/2 + 3/4
= 6/4 + 3/2
= 3/2 + 3/2
= 6/2
= 3.
Multiply the feasible values of the experiment with their probabilities.
At last the expected value is E(y) = 3.
A coordinate is parameter that make a decision of position of a point, the length of a number of line or arc. A list of two, three, and otherwise other coordinates can be used to find the position of a point on a surface, volume, otherwise higher-dimensional area.
The Positive direction stand for positive value for equally x axis and y axis. The x axis value and the y axis value should be positive to transfer towards the positive direction. For each negative change in the axis will not direct to positive direction.
