Recent content by cielo

Thank you so much for your very good idea. Because of that, I already got the E[Y]. Can you still help me in finding the distribution of Y? I am confused about this one I made: P[Y] = \int^{0}_{1} \left[nCy x^{y} (1-x)^{n-y} dx\right] I understand that is a a beta function if we...

Thank you for your good idea Dick! =)

Homework Statement Homework Equations What is the integral of \int^{0}_{1} nCy x^{y} (1-x)^{n-y} dx ? The Attempt at a Solution \left(nCy\right) \int^{0}_{1} x^{y} (1-x)^{n-y} dx

Homework Statement Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations FInd E(y) and the distribution of Y.The Attempt at a Solution f(x) = \frac{1}{b-a} = \frac{1}{1-0}...

However, I'm wondering what is the use of 2 when the integral is just zero?

okay, let me see if I figure this out right. i) The sign of (x-b)f(x) over the interval is positive. ii) The sign of the integral of (x-b)f(x) is positive. iii) Substituting b to m in the expression E(|X-m|) + 2 \int_b^m (x-b) f(x) \, dx results to E(|X-b|) + 2 \int_b^b (x-b)...

I am having a hard time how to evaluate this integral because the function f(x) is not given. \int_b^m (x-b) f(x) \, dx

Homework Statement Let X be a continuous random variable with median m. Minimize E[|X - b|] as a function of b. Hint: Show that E[|X - b|] = E[|X - m|] + 2 \int (x - b) f(x) dx , where the integral is from b to m. Homework Equations The Attempt at a Solution I wanted to try a...

Homework Statement If X is a random variable with density function: f(x) = \lambdae^{-x \lambda}where X>=0.Homework Equations Why is the expected value of X, or E[X] = \frac{1}{\lambda}?The Attempt at a Solution E[X] = \int x*(\lambdae^{- \lambda}^{x}) dx, where the integral is from 0 to...

Homework Statement For matrix X partitioned as \underline{X} = [ \underline{X}1 \underline{X}2 ] with \underline{X}1 matrix full column rank rx, Homework Equations prove that \underline{X}(\underline{X}'\underline{X})^{C}\underline{X} =...

Sorry, there were typo errors...excited in sharing what I've done. Once again, thank you! I sit here corrected.

lanedance, you gave me a very idea in solving this problem. P(x=0) = P(00)=(3/4)*(3/4)=9/16 p(X=1) = p(b0) + P(0b) = (1/4)*(3/4) + (3/4)*(1/4) = 6/16 P(x=2) = P(bb) = (1/4)*(1/4) = 1/16 now the cdf follows: F(x) = o for 0>x F(x) = 9/16 for 0<=x<1 F(x) = 5/16 for...

Praharmitra, thank you for the first one guiding me in this problem!

Thank you for guiding me here. I have constructed this table with the corresponding probability of values. x 0 1 2 f(x) 6/10 3/10 1/10 Is there a general formula for finding the cumulative distribution function and the probability density function specific for this problem? Also, please...

Homework Statement The experiment is to toss two balls into four boxes in such a way that each ball is equally likely to fall in any box. Let X denote the number of balls in the first box. Homework Equations What is the cumulative distribution function of X? The Attempt at a...