I just want to say that I have been working for the USPTO for a while now and never would have considered patents if not for this thread. If anyone has any questions about the USPTO or working as a patent examiner I'll answer what I can.
Yeah, its been several years since I've had any optics classes so I'm struggling to remember. I recall doing some matrix multiplication for compound lenses but I don't dare delve that deeply. I don't think it is impossible, just more effort.
What 'd' should be used for calculating the power when including the third lens? So I have the first two lenses easy enough. But I'm not sure if I take the P12 to be the distance of the second lens, the average of the distance from 1->3 and 1->2 or just the total distance. I suspect it is the...
Homework Statement
I have a compound thick lens problem that I need to find the sign of the refractive power.
Homework Equations
Thick lens equation and focal length equation.
The Attempt at a Solution
I believe all I need to do is calculate the focal length of the first two thick lenses and...
Homework Statement
I am suppose to calculate the relative entropy between two sets of data:
Base set
Set 1:
A C G T
0 0 0 10
0 0 0 10
0 0 10 0
0 10 0 0
10 0 0 0
* * * * //Randomized
0 0 0 10
0 10 0...
I think that I have found a way to do this, but I want to make sure it is correct.
I believe that the equation is telling me to multiply the two probabilities (prob.to be ACGT within R or G and prob. that R or G changed) and then multiply all of those together. I'm just not sure about order...
Homework Statement
Consider an HMM with two possible states, “R” and “G” (for “regulatory” and “gene” sequences respectively). Each state emits one character, chosen from the alphabet {A,C,G,T}.
The transition probabilities of this HMM are:
aRG = aGR = 1/4
aRR = aGG = 3/4
The emission...
Well, the ML method described in class was to take the binomial distribution's derivative, set it to 0 and solve for the probability. So that is the method I used. Is this not correct?
Homework Statement
A strand of length L begins life as all A's. Assume that each letter evolves independent of all the rest until today, 1000 generations later. Within each generation there is a ##\mu## probability that the letter mutates to either C, G, T. Finally, assume that once a letter...
I finally found time to sit and finish this, sorry it took so long. So, I found the maximum with the method I described initially and got the exact some result as if I had just taken the first "simple" method I thought of. It seems my first instinct was correct.
Thanks for the help.
My idea was handle each as either A or Not-A as you mentioned. Since I was explicitly given the hint to use the binomial and maximization likelihood. I don't believe we ever discussed the multinomial distribution but I can see how it works here.
I think that since the problem is really just...
Homework Statement
I have a DNA sequence generated by L throws of a 4 faced die with probabilities ##\pi_A, \pi_C, \pi_G, \pi_T##. Each probability is unknown. Task: estimate the probability of each side of the die. Hint: use a random variable defined by the sequence that has a binomial...
But every value I used for Poissons was already known from my earlier calculations and I didn't use the result for anything.. I feel like I missed something here.... Was I suppose to use the 0.00529 to find the expectation with 1024 strand (1024*.00529=5.42)?
Okay, then using Poisson's:
##P(X)=\frac{\lambda^k e^{-\lambda}}{k!}=\frac{4^{10} e^{-4}}{10!}=0.00592##
So, the probability of 10 occurrences here is just 0.00592.How does this relate to the Z factor though? If the variance is indeed the same as the expectation then my answer is exactly "3" ...
Half correct. THe 1/256 isn't the expectation. Rather it is the probability of finding the 4 letter sequence at any given position within the sequence.
Sorry, I kept getting interrupted as I was writing this (potty training my son). The question is asking just for the "Z-score" (standard...
Homework Statement
I have a 4-letter DNA sequence (AGGA) that appears 10 times in a strand that is 1027 letters long. The probability of finding this sequence at any random position is 1/256. What is the Z-score of this observation?
Homework Equations
##Z=\frac{(X-E(X))}{\sqrt{Var(X)}}##
The...
Oh geez, I dunno why I did that. I got it, now. I'm going to think on this a bit and come back if I have any other questions. This is going to take some amount of googling to figure out.
Thanks for the help, everyone!
I promise I haven't missed a lecture (there was only 1 on this), we just didn't discuss anything in great detail as, apparently, it was expected that I have some background in this.
It makes sense to me that the V(T) is the sum of the variances for each Xn and, likewise, it makes sense that...
I honestly don't know what to do with this. I get that I know the variance of each Xn (1.2). But I don't know the total number of heads for each. I the expected value is 2, I think, but this just brings me in a giant circle. Somehow I need to get E(T) without know any X values... I feel like...
A bit more information then. I'm given the following data:
(I couldnt get a latex table to work on here for some reason)
X:-------- 0---------1---------2---------3---------4--------5
Pr(X): 0.07776 | 0.2592 | 0.3456 | 0.2304 | 0.0768 | 0.01024
X is the number of times heads appears in 5 rolls...
Homework Statement
Coin flip problem. I'm given the probability distribution of how many times a coin is heads out of 5 flips. From this, I need to determine if the following deal is worth it and, if not, how much it costs using variance:
After flipping the coin 20 times I need to pay my...
Homework Statement
What is reduced density matrix ##\rho_A## and the Bloch vector representation for a state that is 50% ##|0 \rangle## and 50% ##\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)##
Homework Equations
The Attempt at a Solution
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I haven't seen many (any?) examples of this so...
Homework Statement
Consider the Hamiltonian ##H=\begin{bmatrix} 0& \frac{-iw}{2}\\ \frac{iw}{2} & 0 \end{bmatrix}##
Write the finite temperature density of the matrix ##\rho(T)##
Homework Equations
##\beta=\frac{1}{kT}##
The Attempt at a Solution
The initial part of the problem had me find...