How to find the expected value of the maximum of n random variables?
However, if we took the maximum of, say, 100 ‘s we would expect that at least one of them is going to be pretty close to 1 (and since we’re choosing the maximum that’s the one we would select). This doesn’t guarantee our math is correct (although it is), but it does give a gut check that what we derived is reasonable.
What should the value of the random variable Y be?
Now, lets define a random variable Y = max(x1, …, xn). When n = 1, the expected value of Y is μ. I would expect that as n increases, the expected value of Y should increase as well.
How to determine the expected value of Y?
Now, lets define a random variable Y = max(x1, …, xn). When n = 1, the expected value of Y is μ. I would expect that as n increases, the expected value of Y should increase as well. Is it possible to determine the expected value of Y for any value of n, in terms of μ and σ?
What is the PDF of a random variable?
PDF is a function that specifies the probability of a random variable taking value within a particular range. Here is the PDF of a continuous random variable that is uniformly distributed between 5 and 10. The x-axis contains all possible values and the y-axis shows the probability of values.
Is the expected value of X and Y the same?
Both X and Y have the same expected value, but are quite different in other respects. One such respect is in their spread. We would like a measure of spread. Definition: If X is a random variable with mean E(X), then the variance of X, denoted by Var(X), 2is defined by Var(X) = E((X-E(X))). A small variance indicates a small spread.
Which is the average configuration of two random points?
This is the “average” configuration of two random points on a interval and, as you see, the maximum value is two-thirds of the way from the left endpoint. Since x and y are independent random variables, we can represent them in x-y plane bounded by x=0, y=0, x=1 and y=1.
How to calculate the value of an indicator variable?
An indicator variable for the event A is defined as the random variable that takes on the value 1 when event A happens and 0 otherwise. A)=1*P(A) + 0*P(AC) =P(A). One-to-one correspondence between expectations and probabilities.