Recent content by ObliviousSage

I'm not sure I understand; don't I need to integrate with respect to T to get the marginal density for U? And the bounds for integration with respect to T should be 0 to 1, right? I want things just in terms of U, with no T. I'm familiar with what you said in the second paragraph, I just...

Oh hey, yeah, that makes that one easy! Thanks Stephen! I totally forgot I didn't need the full probability mass function, just that one particular value.

Homework Statement Problem A: A random variable T is selected from a uniform distribution over (0,1]. Then a second random variable U is selected from a uniform distribution over (0,T]. Determine the probability Pr(U>1/2). Problem B: Suppose 3 identical parts are chosen for inspection. Each...

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Homework Statement A copper rod 90cm long is used to poke a fire. The hot end of the rod is maintained at 103 degrees Celsius and the cool end has a constant temperature of 25C. What is the temperature of the rod 24cm from the cool end? specific heat of copper: c = 387 J/kg*K thermal...

OK, got it now. Thanks for your help guys, I was definitely making it way too complicated before.

OK, that explains it. They both looked right at a glance, and I was sure you could express it either way, but they weren't giving me the same answer so I was getting confused. Doing X3=2X2 and Y=X1+X3 has been way easier for me to visualize, I'm finishing it up now and the answers seem to...

Think I'm making progress this way, but I'm not sure I'm doing it right. Shouldn't my equations for FY(y) for 0<y<1 and for 1<y<2 give the same result at y=1? I got the following to start with: fX1X3(x1,x3) = 1/2 0<y<1 => integral(X3: 0 to y) dx3 * integral(X1: 0 to y-x3) (1/2)dx1 1<y<2 => (...

Talked with someone else who suggested I model it as Y=X1+X3, X3 = X2. I'm going to try working it out that way real quick.

The limits of integration for the outer integral in double integrals like this still don't quite make sense to me; I can usually sort of see why the right answer is right, but I'm not really certain how to get there. The way of defining the limits that seems natural to me keeps setting the...

For 2<y<3, it seems like I need to integrate with respect to X2 from (y-x1)/2 to 1, but then I don't know what the limits of integrate with respect to X1 would be.

Awesome, I wasn't sure. Thanks for clearing that up!

Whoo, math derp! OK, now it comes out to 0.054, the same as the other way, which is good because they both seemed like valid ways of solving the problem. Awesome, thanks for the help!

Two "Sum of Random Variables" Problems Homework Statement Problem A: Consider two independent uniform random variables on [0,1]. Compute the probability density function for Y = X1 + 2X2. Problem B: Edit: never mind, solved this one Homework Equations fY(y) = F'Y(y) FY(y) = double integral...

As described in the first post, two binomial distributions: X represents buying any car, and has n=5, p=7/10, while Y represents someone buying a car choosing a high-end car, and has n=X and p=2/7. Binomial distributions have probability p(k)=(n choose k)*pk*(1-p)n-k. We thus want the...