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.
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.
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.
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.
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.