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  1. Z

    Marginal probability?

    If there are X and Y two random variables. The pdf of Y is f(y), and conditional pdf of X is f(x|y). I want to find the marginal CDF of X, the F(x). Is this correct? F(x)=\int^{F(x|y)}_{-\infty}f(y)dy \dfrac{d}{dx}\int^{F(x|y)}_{-\infty}f(y)dy=\int^{\infty}_{-\infty}f(x|y)f(y)dy=f(x)?
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    Make F RV by using 2 normal?

    I don't know if this is possible or not, let's see if this is a fun problem. Let X_1 and X_2 be 2 independent normal random variables. They have different means and variances, and they are independent. I want to have a function that inputs X_1 and X_2, and it has a F distribution with degree of...
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    Find Interval for Coefficients

    For a simple linear model: \alpha+\beta\times x=y If it is observed that y \in (-8.51,23.20) given x=4 The question is to give intervals of \alpha, \beta, which satisfy y \in (-8.51,23.20) given x=4. Is this problem identifiable? Can it be found the unique intervals for \alpha...
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    Solve for Interval Problem

    Hi all: The inequality here involves abs, and max functions, how to solve for the interval as show below?
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    What is the fair gamble price?

    Say, I'm a bookkeeper of a gamble of flip coin. The price for each trial is 0.5, i.e. if there is a head I pay gambler 0.5, otherwise I get 0.5 from the gambler. There are only 10 flips or trials in the game, so that each gamble only can play 10 trials. I know to choose the 0.5 as the fair...
  6. Z

    Game Theoretic Proability

    Hi all, I want to learn Game-Theoretic Probability. I have found few examples of computing conditional probability by game theoretic approach. Is there and good readable tutorial could show help me to learn this topic and conformal predictions? Let's recover this lost philosophy of...
  7. Z

    How to show this sum covereges

    \sum_{m=1}^N(\frac{1}{m^4}-\frac{1}{m^6}) My math on sum series is very rusty, can anyone show me show this sum converges? It is not geometric series, right? Suddenly found out it is needed to show Kolmogorov SLLN of some random varianble. Thanks in advance
  8. Z

    Any function is not a Random Variable

    There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables. If you know functions are not random variables please please reply this post. This class is about set theory, probability measure, Borel...
  9. Z

    Heaviside Function

    Hi all: The Heaviside function multiples a random varaible, is that a probability density function? This is my first time knowing about Heaviside, any tutorial and application of it?
  10. Z

    Jacobian Matrix of Residuals

    There are 2 parameters in the Gamma distribution, alpha and beta. If sample 500 of the Gamma random variable, there unbiased mean and variance can be estimated by the sample moments. If it is also interested to estimate the variance and covariance of the parameters, alpha and beta; Jacobian...
  11. Z

    How deep Sets affect Measure Theory?

    Guys, I'm taking real analysis starting with open, close, compact sets, and neighborhoods. Now I'm addict to rely on these concepts to do my proofs. In the future I will have to take Measure Theory. Can anyone give me a percentage indication for how many percent theorems are proven by the set...
  12. Z

    Are there any good introductory textbook to cover all these topics?

    Linear Spaces Norms and inner products Holder’s inequality Minkowski’s inequality Normed linear spaces Cauchy sequences and complete spaces Banach spaces Reitz representation theorem Hilbert spaces Orthogonal bases Generalized Fourier expansions Lebesgue Measure and...
  13. Z

    Heine Borel Theorem

    The implications of Heine Borel Thm are not immediate to me. Any results are derived from this theorem?
  14. Z

    Vector Space, and Normed Vector Space

    Hi all, It has been very useful of posting my questions here to help me pushing through the book reading of analysis. This forum is a perfect place and the best place for people who are interested in knowledge and the beauty of knowledge. Here goes another question from me. All continuous...
  15. Z

    Heine Borel Theorem, why I need it?

    Hello all: Closed interval subcover is finite. How do I use it? Why should anyone on earth proved things like this? Please give me the significance of this technological development. Thanks, zli034
  16. Z

    Ordered Field?

    Could anyone explain me the concept of Ordered Field? I have googled it, all came up are definitions I don't know how to handle. Numbers and calculations with statistical means I can understand fairly simple; but pure math has never worked for me. Can anyone make the ordered field with...
  17. Z

    Replication Method for Survey Estimation

    Hi all, What is a good way to use replication methods for estimation? For a dataset with no design information, only weighting remain. I know the basic principles of replication. Are there any considerations to use replication effectively? There is a public data of 15,000 people from the...
  18. Z

    Zoom in is equivalent to move forward?

    For the digital cameras, is the zoom-in is equivalent to move forward the camera? My simple camera gives me 5 level zoom in, it has 3X optical zoom, but it takes me to press the button 5 times to reach the highest limit. Can I determine the forward distance of each zoom-in button pressed...
  19. Z

    Estimate distance to stars?

    Think about this, a photon travel through the universe, its path can be reflected by other objects, bended by gravity. Therefore the path would not be a straight line anymore. But very often from the TV science shows stating the distances to other stars are some some million light years. How...
  20. Z

    Stargazing How to estimate distance by a telescope

    Guys I don't know if people could estimate distance to a target object by looking through a telescope. I believe telescopes for this kind use must be calibrated some how. When the time people sailed in the ocean and when they spotted another boat by the telescope, how did they tell the...
  21. Z

    Variance of Quadratic Form

    In the Searle's 1971 book Linear Model, page 57, has a formula for the Variance of Quadratic form: var(Y^{T}AY)=2tr(A\SigmaA\Sigma)+4\mu^{T}A\SigmaA\mu The proof of this showed on page 55 was based on MGF. I'm looking for proofs are less complicated. Some thing that is similar to show the...
  22. Z

    Find a tangent line?

    Say I have a curve is called C: y=1287*x^-1.5 Find a tangent line to the C, and the tangent line has to have a intercept of 150. This is not a homework, not at all.
  23. Z

    Sum of 2 Non-identical Uniforms RVs?

    Does anyone know to formulate the pmf and pdf of sum 2 uniform random variables of non-identically distributed? Say rv X is uniformly distributed range (0,1), and rv Y is uniformly distribute range (-9,0). For Z = X+Y, what is the probability distribution of Z? Thanks in advance. So many...
  24. Z

    Joint Probability of Sum Normal

    Don't know there are anyone can help me out with this. This is just something I asking myself, not a homework I must say. Let's define X and Y are 2 standard normal random variables. And random variable Z=X+Y. For real number a, we know P(X>a), the probability of X is greater than the...
  25. Z

    Bayesian Network for Continuous Random Variable?

    There are no Bayesian Networks for continuous random variables, as far as I know. And the Netica Bayesian Network software discretize continuous random variables to build bayesian models. Are there any reasons for this? Has anyone proposed continuous random variable bayesian networks?
  26. Z

    Test on correlation?

    Say I have 2 separate predictor variables x and y. And the response variable is z. The correlation between x and z is a; the correlation between y and z is b. How to get the p-value for a = b? By using SAS or SPSS. I believe we should use t-test. Because the correlation analysis for...
  27. Z

    Mean of Exponential RVs

    I forgot how to derive the mean of exponential random variables follow the chi square distribution with degree freedom 2n. Don't know where I got it wrong. Anyone have a clue how to do it? Thanks
  28. Z

    Is this contains an open set?

    On the number line R, does [-1,\infty) contain an open set? because it includes -1, don't think it is an open set.
  29. Z

    Product of expectations?

    say, E(1/x)=a and E(y)=b. a and b are constants and x and y are random variables. Can I say E(y/x)=b/a? Thanks.
  30. Z

    Unbiased estimator of a probability?

    Say, x_1{}... x_n_+_1{} are iid Bernoulli random variables with parameter p. I want an unbiased estimator for probability Pr(\Sigma_{} x_1_._._._n{} > x_n_+_1{} ) I have failed to establish E(1 - \Pi x_i{}) is unbiased estimator for the probability. Any hints? thanks.
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