Recent content by dspampi

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...

I'm having trouble understanding the boundary conditions and when you would need to use Bessel vs Modified Bessel to solve simple cylindrical problems (I.e. Heat conduction or heat flow with only two independent variables). When do you use Bessel vs Modified Bessel to solve Strum-Louville...

I was able to do the first part of this problem but unsure how to approach this: Mendel, revisited: Mendel’s peas had either purple or white flowers; flower color is due to a single gene, for which the purple allele (A) is dominant to the white allele (a). We cross two pure-breeding lines...

I was wondering if someone could help me go through a simple example in using Green's Function. Lets say: x' + x = f(t) with an initial condition of x(t=0,t')=0; Step 1 would be to re-write this as: G(t,t') + G(t,t') = \delta(t-t') then do you multiply by f(t')\ointdt' ? which I...

Consider the following experiment: a coin that lands heads with probability p is flipped once; if on this first flip it came up H, it is then repeatedly flipped until a T occurs; else, if on the first...

Give an example of a random variable (i.e. give the range of values it takes and its p.m.f.) with the following properties: EX = 4, VAR(X)=4. Now give an example of a random variable with a different p.m.f. than...

In this problem, assume researchers have constructed a risk score for HIV for the U.S. population, which is a function of risk factors such as frequency of unprotected sex, use of intravenous drugs, having another sexually trans- mitted infection, etc. Assume each risk factor measured is...

Or I suppose what would make more sense would be: (10C0) (.6)^10*(.4)^0 + (10C2) (.6)^8*(.4)^2 +...(10C10) 1*(.4)^10 ?

Ok well I agree that all 5 dice are being rolled at the same time so I think regardless that P(win) = 6/6 * 5/6 * ... * 2/6 = 6!/6^5 and P(lose) = 1 - P(win) = 0.907407407 So to calculate the rolls that I have lost down to 1%, is that just (P(lose))^n = 1?

Ok so let see if I finally get this. So for (A) I add up the probability of getting HH and TT Which would be (.6)^2 + (0.4)^2 For (C) now there are 6 possibilities to get an even number of heads. So does that mean its simply (10C6) (.6)^6*(.4)^4 I have a feeling that this is wrong and I'm...

Consider the experiment of rolling 5 fair dice. You “win” if all the dice show different numbers. I have to decide in advance how many times to repeat the experiment. I will be very happy if I win at least once. What is the least number of times I need to plan to repeat the experiment so that...

A biased coin that lands heads with probability 0.6 is flipped 2 times. a. What is the probability of getting an even number of heads? b. Given that more heads than tails appear, what is the probability that all of the flips are H? c. same as (a) except now the coin is flipped 10 times...

Find a particular solution for the following non-homogeneous dieren- tial equation by the method of undetermined coefficients: a. y'' + 8y' +12y = e^-2x + sin(2x) b. y'' + 11y' - 12y = 3x^2 + 4 + e^x I got for a. Yp(x) = 1/4xe^-2x + 1/40cos(2x) +1/20 sin(2x) b. Yp(x) = -1/4x^2...

Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. The group is split in half at random. What is the probability that each half contains exactly N women and N men? And the second part asks for a given N, set up Stirling's Formula so you can calculate the...