Recent content by gajohnson

They were not given but, thankfully, because they are independent, the only covariances that are not 0 are those that are just a covariance with itself, i.e. the variance already given--usually multiplied by some constant.

I was visualizing it properly but not connecting the obvious dots, thanks everyone!

Homework Statement Consider the bivariate density of X and Y, f(x, y) = pi/2 for x^2 + y^2 ≤1 and y > x and = 0 otherwise. (a) Verify that this is a bivariate density (that is, the total volume ∫∫ f(x,y)dxdy = 1) Homework Equations The Attempt at a Solution The problem I'm having is...

Oh, boy...I seem to have missed the "independent" condition in the problem. It works out nicely that each combination seems to have a random variable with a covariance of itself somewhere in there. The rest all becomes 0s. Thanks!

Homework Statement Suppose that X1, X2, and X3 are independent random variables with variances 3, 4, and 8, respectively. Let Y1 = 2X1 + 3X2, Y2 = X3 – X2, and Y3 = X1 + X2 + X3. (a) Using the general relationship Cov(W+X, Y+Z) = Cov(W,Y) + Cov(W, Z) + Cov(X, Y) + Cov(X, Z), find...

I look forward to discovering more about this wonderful thing. Thanks for your insight!

I am indeed aware of the importance of the memoryless property of the exponential (although likely not to the extent that you are), and this is precisely why it seemed to me that there was a trick involved. I don't know quite how I gave off the impression that I thought the memoryless...

Confirmed this elsewhere. It is indeed that simple. Appreciate your help!

Yes, of course. But it works out pretty simply that the distribution of W is the same as the distribution of Z. Thanks for confirming this for me. Sometimes something seems so simple that I question it--an instance of trying to disentangle actual mathematical results from the intentions of those...

Homework Statement Suppose that the waiting time for the CTA Campus bus at the Reynolds Club stop is a continuous random variable Z (in hours) with an exponential distribution, with density f(z) = 6e–6z for z ≥ 0; f(z) = 0 for z < 0. (a) What is the expected waiting time in minutes (the...

So much simpler! My trig is too rusty. Ok, so then I find that g(Y)=arctan(Y) and, after taking the derivative, I make the transformation assuming the uniform distribution described before for X. I get f_Y(y)=1/{\pi}(1+y^2) Is it that simple? Thanks!

Homework Statement Consider a two-ended laser spinner; that is a pen-like laser acting as the arrow mounted on a pin at the center of a spinner. Suppose the center of the disk is one meter away from a wall of infinite extent marked with a linear scale, with zero at the point closest the center...

I believe that a lot of these companies (in particular social media) try to achieve network effects, which are a very powerful force in determining the terrain of tech industries. For instance, consider what Google is trying to do over the last few years. No longer is Google simply a place to...

Ah, of course. Got it. Thanks!

Homework Statement This isn't really a homework question, just working through Rudin and got caught up on something. C(x) and S(x) refer to cos(x) and sin(x) respectively. Here is the section in question: http://grab.by/mSo8 Homework Equations The Attempt at a Solution Well the part I'm...