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- 03:27, 10 May 2014 (diff | hist) (+13) Elad Segment 19 (current)
- 03:26, 10 May 2014 (diff | hist) (+539) N Elad Segment 19 (Created page with "1. Let <math> y = x - \mu </math> which means it is normal as well with mean <math>0</math> and covariance <math>\Sigma</math>. Let <math> y^* = L^{-1}y</math>. It is easy to ...")
- 03:20, 10 May 2014 (diff | hist) (+21) Elad Liebman (current)
- 03:13, 10 May 2014 (diff | hist) (+18) Elad Segment 15 (current)
- 03:12, 10 May 2014 (diff | hist) (+527) N Elad Segment 15 (Created page with "1. Let's check. Results: N2: (370, 23, 0.003, 7.8209671637933636e-23) N11: (333, 5, 0.003, 0.003575961701113451) N13: (120, 4, 0.003, 0.00050434683852936565) Using this code...")
- 03:01, 10 May 2014 (diff | hist) (+171) N Elad Segment 22 (Created page with "1. Well, the gradient of f now is <math> (0,0,1/b_5, 0, -\frac{b_3}{b^2_5})</math>, which means we can derive the variance to be ~0.014 and the standard error to be ~0.12.") (current)
- 02:56, 10 May 2014 (diff | hist) (-48,034) Elad Liebman
- 02:55, 10 May 2014 (diff | hist) (+2,356) N Elad Segment 40 (Created page with "== Segment 40 Problems == 1. OK, so I implemented the code as in lectures 40 (and 31) - I had some trouble with the Hessian not being PSD but I think I overcame that, obtaini...") (current)
- 02:54, 10 May 2014 (diff | hist) (+1,451) N Elad Segment 39 (Created page with "== Segment 39 Problems == 1. Let's first look at the transition probability matrix, which is: <math>T_{x_1\rightarrow x_2} = \begin{matrix} 0 & 1 & 0 & 0 & 0 \\ 0.5 & 0 & 0.5...") (current)
- 02:54, 10 May 2014 (diff | hist) (+992) N Elad Segment 34 (Created page with "== Segment 34 Problems == 2. This actually raises an interesting question - what's the procedure for generalizing the Wald statistic for >2 columns? My most immediate respons...") (current)
- 02:54, 10 May 2014 (diff | hist) (+1,795) N Elad Segment 33 (Created page with "== Segment 33 Problems == 1. Seemingly it's like dividing N balls in MxN bins, i.e. C(N+MxN-1,MxN-1). But that's only if the columns and rows are not interchangeable. If they...") (current)
- 02:53, 10 May 2014 (diff | hist) (+642) N Elad Segment 32 (Created page with "== Segment 32 Problems == 1. Well, given the null hypothesis, the chance of getting a baseball team with 1 women or less given the circumstances is (C(20,1)*C(80,9)+C(80,10)/C...") (current)
- 02:53, 10 May 2014 (diff | hist) (+2,015) N Elad Segment 30 (Created page with "== Segment 30 Problems == 1. Good old Jensen's inequality, a trusted friend. Like Cauchy-Schwartz. Anyway, to business: a) Let <math> f(x) = x^2 </math>. This function is ob...") (current)
- 02:52, 10 May 2014 (diff | hist) (+2,434) N Elad Segment 28 (Created page with "Elad Segment 28 == Segment 28 Problems == 1. Attached is the code for fitting GMMs in 1-d (based of course on the lecture slides). ====function bla = fitGMM1d(means, var...") (current)
- 02:52, 10 May 2014 (diff | hist) (-2,436) Elad Segment 27 (current)
- 02:51, 10 May 2014 (diff | hist) (+3,761) N Elad Segment 27 (Created page with "== Segment 27 Problems == 1. <math> P(x|\beta, c) = c \beta exp(-\beta x) + (1-c)\frac{2/\pi}{1+x^2}</math> 2. So given x values, the maximum likelihood values of beta and c...")
- 02:50, 10 May 2014 (diff | hist) (+2,439) N Elad Segment 20 (Created page with "== Segment 20 Problems == 1. If we have a set of functions <math>X_k(x)</math> and a set of coefficients <math>b_k</math>, once we have pairs of samples and values (or "label...") (current)
- 02:38, 10 May 2014 (diff | hist) (+900) N Elad Segment 16 (Created page with "== Segment 16 Problems == 1. Running the following procedure 1000000 times: a) get 50 random values in [0,1]; b) Apply the BH-FDR procedure; c) count number of significant di...") (current)
- 02:37, 10 May 2014 (diff | hist) (+1,263) N Elad Segment 14 (Created page with "== Segment 14 Problems == 1. In a two-sided test, the p-value of getting 8 out of 10 of any specific side if all rollouts are equal (since p=0.5) reduces to counting the poss...") (current)
- 02:37, 10 May 2014 (diff | hist) (+1,459) N Elad Segment 13 (Created page with "== Segment 13 Problems == 1) We can approximate the Binomial distribution B(n,p) with the Normal distribution N(np, np(1-p)). Trivially, this approximation is worst when n=1,...") (current)
- 02:36, 10 May 2014 (diff | hist) (+885) N Elad Segment 12 (Created page with "== Segment 12 Problems == 1. We need to look at the inverse of the t cdf at <math>P=0.025,P=0.975</math>. Since the size of the critical region scales linearly with <math>\si...") (current)
- 02:36, 10 May 2014 (diff | hist) (+1,866) N Elad Segment 11 (Created page with "== Segment 11 Problems == 1) <math> f(x, \mu, \sigma) = y = \frac{1}{\pi\sigma}(1 + (\frac{x - \mu}{\sigma})^2)^-1 \Rightarrow \frac{1}{y} = \pi\sigma (\frac{x - \mu}{\sigma})...") (current)
- 02:36, 10 May 2014 (diff | hist) (+444) N Elad Segment 10 (Created page with "== Segment 10 Problems == 1) We'll just use the CLT, and using the fact that the variance of a uniform continuous distribution is <math>\frac{(b-a)^2}{12}</math> (easy result...") (current)
- 02:35, 10 May 2014 (diff | hist) (+1,159) N Elad Segment 9 (Created page with "== Segment 9 Problems == 1) Let <math>X,Y</math> be two normal distributions whose variables are drawn as follows: <math> x \sim N(\mu_1, \sigma_1), y \sim N(\mu_2, \sigma_2)...") (current)
- 02:16, 10 May 2014 (diff | hist) (+530) N Elad Segment 8 (Created page with "== Segment 8 Problems == 2) To find the mode we need to derive and equate to <math>0</math>. Notice the normalizing factor isn't dependent on <math>x</math> so we can omit i...") (current)
- 02:15, 10 May 2014 (diff | hist) (+463) N Elad Segment 7 (Created page with "1) Trivially, <math> \frac{d(E[x^2] -2aE[x] + a^2)}{da} = -2E[x] + 2a \Rightarrow -2E[x] + 2a = 0 \Rightarrow E[x] = a </math>. This is possible because of the linearity of ex...") (current)
- 02:14, 10 May 2014 (diff | hist) (+2,395) N Elad Segment 6 (Created page with "== Segment 6 Problems == 1) I'm not sure I follow the question. Is it just <math>bin(n,N,r) = {N \choose n}\cdot r^n \cdot (1-r)^{N-n}</math>? 2) What seems to be wrong (and ...") (current)
- 02:13, 10 May 2014 (diff | hist) (+4,838) N Elad Segment 5 (Created page with "== Segment 5 Problems == 1) There are 5 prime numbers in range 1 to 12 (2,3,5,7,11). There are 15 possible dice rolls to get any of these numbers (1 + 2 + 4 + 6 + 2, respecti...") (current)
- 02:13, 10 May 2014 (diff | hist) (+1,579) N Elad Segment 4 (Created page with "== Segment 4 Problems == 1) <math> \int_0^1 \delta(3x-2)dx = \int_{-2}^{1} \delta(y)dy = 1 </math> 2) <math> \int \delta(ax)dx = \int \delta(u)\frac{du}{a} = \frac{1}{a} \de...") (current)
- 02:12, 10 May 2014 (diff | hist) (+8,525) N Elad Segment 3 (Created page with "== Segment 3 Problems == 1) We can simply enumerate all cases and marginalize. We have 6 scenarios - 3 options for doors for us to pick times 2 options for Monty to open a do...") (current)
- 02:12, 10 May 2014 (diff | hist) (+4,118) N Elad Segment 2 (Created page with "== Segment 2 Problems == 1) Let's just calculate using Bayes' Theorem. The chance of being in H1,H2,H3 given that we've observed a troll is: <math>P[H1|G] = \frac{\frac{3}{5}...") (current)
- 02:11, 10 May 2014 (diff | hist) (+2,166) N Elad Segment 1 (Created page with "== Segment 1 Problems == 1) Trivially, P(ABC) = P(BCA) = P(B)P(CA|B). Now,algebraically, P(CA|B) = P(C|B)*P(A|BC). Therefore we get P(ABC) = P(B)*P(C|B)*P(A|BC), as required. ...") (current)
- 12:53, 30 April 2014 (diff | hist) (+1,938) Elad Liebman
- 12:48, 30 April 2014 (diff | hist) (0) N File:Wald cs chisquare Elad.png (current)
- 06:22, 30 April 2014 (diff | hist) (+592) Elad Liebman
- 21:43, 29 April 2014 (diff | hist) (+262) Elad Liebman
- 20:14, 29 April 2014 (diff | hist) (+1,231) Elad Liebman
- 21:23, 28 April 2014 (diff | hist) (-17) Elad Liebman
- 02:52, 28 April 2014 (diff | hist) (+2,376) Elad Liebman
- 01:54, 28 April 2014 (diff | hist) (0) N File:Exon1 elad.jpg (current)
- 01:53, 28 April 2014 (diff | hist) (0) N File:Exon2 hist elad.jpg (current)
- 01:53, 28 April 2014 (diff | hist) (0) N File:Ex1 areaRat elad.jpg (current)
- 13:58, 26 April 2014 (diff | hist) (+23) Elad Liebman (→Segment 39 Problems)
- 13:51, 26 April 2014 (diff | hist) (-1) Elad Liebman (→Segment 39 Problems)
- 13:51, 26 April 2014 (diff | hist) (+27) Elad Liebman (→Segment 39 Problems)
- 13:47, 26 April 2014 (diff | hist) (+5) Elad Liebman
- 13:46, 26 April 2014 (diff | hist) (+1,190) Elad Liebman (→Segment 39 Problems)
- 13:37, 26 April 2014 (diff | hist) (0) N File:39 2 el.jpg (current)
- 12:43, 26 April 2014 (diff | hist) (+1) Elad Liebman (→Segment 39 Problems)
- 12:42, 26 April 2014 (diff | hist) (+2) Elad Liebman
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