What is the expected value of a uniform random variable?

What is the expected value of a uniform random variable?

SOLUTION. Or, in other words, the expected value of a uniform [α,β] random variable is equal to the midpoint of the interval [α,β], which is clearly what one would expect.

How do you find the MGF of a uniform distribution?

Moment Generating Function of Continuous Uniform Distribution

1. Then the moment generating function of X is given by: MX(t)={etb−etat(b−a)t≠01t=0. Proof.
2. From the definition of the continuous uniform distribution, X has probability density function: fX(x)={1b−aa≤x≤b0otherwise.
3. First, consider the case t≠0. Then:

What is the expected value of the max of two dice?

Therefore, the expected value of the max is (1 + 2*3 + 3*5 + 4*7 + 5*9 + 6*11) / 36 = 161/36.

When two dice are rolled the maximum total on the two faces of the dice will be?

Answer: When two dice are thrown simultaneously, thus number of event can be 62 = 36 because each die has 1 to 6 number on its faces.

What is expected value of uniform distribution?

For a random variable following this distribution, the expected value is then m1 = (a + b)/2 and the variance is m2 − m12 = (b − a)2/12.

Which is the expected value of maximum of uniform random variables?

Then consider that you’ll have 1 minus this value, so for your problem you’d have: a = 200, b = 600 and then 1 − F(y) = 1 if x < 200, 1 − F(y) = 0 if x > 600 and 1 − y − 200 400 when y ∈ [200, 600]. So the part you are missing in your calculations is:

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.

What is the expected value of max ( x, y )?

If I have two variables X and Y which randomly take on values uniformly from the range [a, b] (all values equally probable), what is the expected value for max (X, Y)? As soon as X and Y are independent, P( max (X, Y) ⩽ z) = P(X ⩽ z)P(Y ⩽ z).

Which is the best trick for uniform distribution?

There is one trick useful for uniform distribution. The trick: If you have 500 independent uniform random variables on [0; 1] then you may think that you have 501 independent uniform random variables on a circumference with unit length.