Finding Expected Value of fy(Y) = 3(1-y)^2

In summary, the expected value of fy(Y) is the average value obtained when repeatedly sampling the random variable Y. To find it, the formula E[fy(Y)] = ∫fy(Y)*P(Y)dy is used, where fy(Y) is a function and P(Y) is the probability density function of Y. The purpose of finding the expected value is to determine the central tendency or average value of Y for making predictions and decisions. The expected value can be negative if the probabilities and outcomes result in a negative value. The function fy(Y) affects the expected value by determining the possible outcomes and their probabilities.
  • #1
semidevil
157
2
ok, so to find the expected value of fy(Y) = 3(1-y)^2 for 0 <= 1 <= 1

I thought the formula is y * fy(Y) which is the intgeral from 0 to 1 of y* 3(1-y)^2. right?

the book says the answer is 1/4...but I get a whole number answer...
 
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  • #2
Hi,

I did the integral of y*f(y) from 0 to 1 and got the answer 1/4...double check your calculation...This is what I did:

Int[3*(1-y)^2] = 3*Int[y^3-2y^2+y] from 0 to 1
 
  • #3
oops, I forgot the y in the 1st integral expression
 

1. What is the expected value of fy(Y)?

The expected value of fy(Y) is the average value that is expected to be obtained when the random variable Y is repeatedly sampled. It is calculated by taking the sum of all possible outcomes of fy(Y) multiplied by their respective probabilities.

2. How do you find the expected value of fy(Y)?

To find the expected value of fy(Y), we use the formula E[fy(Y)] = ∫fy(Y)*P(Y)dy, where P(Y) is the probability density function of the random variable Y. In this case, fy(Y) = 3(1-y)^2, so we can plug it into the formula and integrate to find the expected value.

3. What is the purpose of finding the expected value of fy(Y)?

The expected value of fy(Y) gives us an idea of the central tendency or average value of the random variable Y. It is useful in making predictions and decisions based on the outcomes of Y, as it represents the most likely outcome.

4. Can the expected value of fy(Y) be negative?

Yes, the expected value of fy(Y) can be negative if the probabilities of the outcomes are such that the sum of the outcomes multiplied by their probabilities results in a negative value. This is dependent on the specific values of fy(Y) and the probabilities assigned to each outcome.

5. How does the function fy(Y) affect the expected value?

The function fy(Y) affects the expected value by determining the possible outcomes and their respective probabilities. In this case, fy(Y) = 3(1-y)^2 represents a parabola with a maximum value of 3. The probabilities of the outcomes can be adjusted to increase or decrease the expected value accordingly.

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