1. ### I Two vectors and two perpendicular lines

In ##\mathbb{R}^2##, there are two lines passing through the origin that are perpendicular to each other. The orientation of one of the lines with respect to ##x##-axis is ##\psi \in [0, \pi]##, where ##\psi## is uniformly distributed in ##[0, \pi]##. Also, there are two vectors in...
2. ### I Conditional distribution of geometric series

Can someone help me on this question? I'm finding a very strange probability distribution. Question: Suppose that x_1 and x_2 are independent with x_1 ~ geometric(p) and x_2 ~ geometric (1-p). That's x_1 has geometric distribution with parameter p and x_2 has geometric distribution with...
3. ### I Compatibility of MWI with probability of outcomes

Can MWI account for the probabilities of outcomes? If MWI says all outcomes are realized, is the probability that an outcome occurs then not 100%? How is this explained with the entanglement of the measured object and the measurement apparatus?
4. ### I Bernoulli Trials Homework Problem

this is the answer Is this right?
5. ### B Fun with (im)probabilities

Hi folks - I need some help with a tricky probability. Here's the situation: Let's say there are 4M internet users in Age Group A. (The total set) Of those 4M, there are 1,000 users who play a specific sport. Those 1,000 are spread evenly over 125 teams, so 8 players each. 1. What's the...
6. ### Tricky problem from Probability

I decided to take cases.For example-:A gets one 1 duck and B gets 2,3,4,...,51.So i can write this as 50C1(1/2)5051C2(1/2)51+50C1(1/2)5051C3(1/2)51+... But i was unable to solve it further. please help.
7. ### B Poisson Distribution - Selecting cookies that are indistinguishable

Here's the problem: A chef made 500 cookies randomly mixed with 1000 nuts including 600 almonds and 400 hazelnuts in which each nut is the same size. Suppose the number of pieces of nuts in a piece of cookie follows a Poisson distribution. (a) Suppose cookies are randomly selected one-by-one...
8. ### Measurements of GHZ state

Here's what I think I understand: First off, the GHZ state ##|GHZ \rangle = \frac {|000\rangle+|111\rangle} {\sqrt 2}##, and ##\sigma_x## and ##\sigma_y## are the usual Pauli matrices, so the four operators are easy to calculate in Matlab. I'm thinking the expectation values of each operator...
9. ### Transition Probability

I set hN(1)hN(1) equal to cNcN, but I'm confused on how I'd be able to solve it and because of that I was not able to conclude that 0 is recurrent when qx/px = infinity
10. ### I On the width of the kinetic energy distribution of a gas

In these lecture notes about statistical mechanics, page ##10##, we can see the graph below. It represents the distribution (probability density function) of the kinetic energy ##E## (a random variable) of all the gas particles (i.e., ##E=\sum_{i}^{N} E_{i}##, where ##E_{i}## (also a random...
11. ### B Conditional Probability

1. Definition If E and F are two events associated with the same sample space of a random experment, the conditional probability of the event E given that F has occurred, i.e. P(E|F) is given by P(E|F) = (E∩F)/P(F) (P≠0) 2. Properties of conditional probability Let E and F be events of...

13. ### Calculating general normal random probability

a) P(X<18) = (18-20)/sqrt25 =-2/5 =-0.4 then you use the standard normal table and find that; P(X<18)=0.3446 b) P(X>27) = (27-20)/5 = 7/5 = 1.4 P(Z>1.4) =P(Z<-1.4) =0.0808 C) =(13<X<23) =13-20/5 , 23-20/5 =-7/5 , 3/5 =-1.4 , 0.6 P(Z<0.6)-P(Z<-1.4) =0.7257-0.0808 =0.6449
14. ### I Are these events independent?

Hello everyone. Let us consider 3 events A,B,C such that: $$P((A \cap B )\cup C)=P(A)*P(B)*P(C)$$ Notice that the second term is a union and not an intersection. Are they independent? And what if the assumption was: $$P(A \cap( B \cup C))=P(A)*P(B)*P(C)$$? I know that the independence condition...
15. ### I How to understand this property of Geometric Distribution

There is a property to geometric distribution, $$\text{Geometric distribution } Pr(x=n+k|x>n)=P(k)$$. I understand it in such a way: ##X## is independent, that's to say after there are ##(n+k-1)## successive failures, ##k## additional trials performed afterward won't be impacted, so these ##k##...
16. ### B LoLN and probability

Does an ensemble of measurements yielding outcome A or B yield an approximation to the probability of A and B, or is such an ensemble of measurements something totally different from probability?
17. ### I Getting the probabilities right

If we have a jar with 3 blue balls and 7 white balls, we say that the probability of blindly getting a blue ball out of that jar is 30%. If we have a jar with 2 blue balls and 8 white balls, we say that the probability of blindly getting a blue ball out of it is 20%. Now if we carry out 10...
18. ### Probability of being in a state is given, Find the normalised wavefunction

Should I treat ψ1 as ψ and ψ 2 as ψ*?
19. ### Probability: distribution, cumulative distribution

I came across this problem in my assignement but I don't really understand the question. The lectures notes handed out by the teacher does not use the term cumulative distribution. Wikipedia says that a cumulative distribution function is the same as a distribution function.
20. ### How can I determine the random variables for this problem?

So i first need to come up with the sample space, X, and Y. Well I would guess that the random variables here are N1 and N2 and thus X = N1 and Y = N2. Now i need to make these random variables a function of L. I dont know what L should be but I would guess it is the outcome of a 1ms interval? I...
21. ### Neutron's crow flight distance & 2° moment of a distribution

Hi, I'm looking for a simple explanation of the meaning of the crow flight distance and why it is defined as the second moment of a probability distribution: $$\bar r^2 = \int r^2 p(r)dr$$ Where ##p(r)## is the probability that a neutron is absorbed in the interval ##dr## near ##r##. And what...
22. ### I David Deutsch (1985) attempt to solve the incoherence problem

Can anyone elaborate on Deutsch's attempt to solve the incoherence problem? He postulates a continuously infinite set of universes, together with a preferred measure on that set. And so when a measurement occurs, the proportion of universes in the original branch that end up on a given branch...
23. ### Power of noise after passing through a system h(t)

**Reposting this again, as I was asked to post this on a homework forum** 1. Homework Statement Hi, I am trying to solve this math equation (that I found on a paper) on finding the variance of a noise after passing through an LTI system whose impulse response is h(t) X(t) is the input noise...
24. ### I White noise & 1/f noise after a system h(t)

Hi, I am trying to solve this math equation on finding the variance of a noise after passing through a system whose impulse response is h(t) X is the input noise of the system and Y is the output noise after system h(t) if let's say variance of noise Y is σy2=∫∫Rxx(u,v)h(u)h(v)dudv where...
25. ### Insights The Sum of Geometric Series from Probability Theory - Comments

Greg Bernhardt submitted a new blog post The Sum of Geometric Series from Probability Theory Continue reading the Original Blog Post.
26. ### B Help with determining the order

Hello guys, Ive been struggling on determining whether something is ordered or unordered. The example i get is something like, "a burger with pickles, tomato, beef will be the same regardless of the way you make the order." Then in this case it would be ordered right? So when something is...
27. ### I Joint PDF and its marginals

Hi all, I was wondering if there exist any theorems that allow one to relate any joint distribution to its marginals in the form of an inequality, whether or not ##X,Y## are independent. For example, is it possible to make a general statement like this? $$f_{XY}(x,y) \geq f_X (x) f_Y(y)$$...
28. ### Two teams, A and B, are playing a series of games

My attempt I used negative binomial to solve the problem, however I'm left with a polynomial that is difficult to solve? Is there any other way to approach this problem? I used the inequality because I'm trying to find the range of p. Since the probability of winning the series for team...
29. ### I Probability-To-Exceed (PTE) and Chi^2 distribution

I would like to know the difference between the ##\chi^{2}## distribution and the PTE (Probability-To-Exceed) ? I must compare 2 data sets A and B and in the article I am reading, they talk about this PTE : For the moment, I only know the ##\chi^{2}## distribution with ##k=2## degrees of...
30. ### How to read a joint discrete table?

Homework Statement [/B] Given a group of 100 married couples, let X1 be the number of sons and X2 the number of daughters the couple has. P(X1 = 0, X2 = 2) = f(0, 2) = 8 /100 = 0.08 2. Homework Equations The Attempt at a Solution I tried to look for a similar example online, I found this...