# Tagged Questions

Questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution.

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### Bivariate normal distributed vector $X (X,Y)$. Show distribution of $(X-Y, X+Y)$.

I have a a bivariate normally distributed random vector $X = (X,Y)$ and with Expected Value $(X)= (\mu(x),\mu(y))$, and Covariance Matrix $2\times 2$. (not independent) Now I want to show which ...
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### Nonstandard normal distribution

I want to understand how to prove results regarding the relationship between the standard and nonstandard normal distributions. In other words, I want to prove the results regarding how to use z ...
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Let $X_1, X_2, · · · , X_n$ be a random sample of size n from a geometric distribution withpmf $f(x) = 0.75 · 0.25^{ x-1} , x = 1, 2, 3, ··· .$ (a) Find the mgf $M_{Y_n} (t)$ of $Y_n = X_1 + ... 1answer 35 views ### Distribution of residual term in regression. In regression analysis for classical linear regression model the residual term is independent of x and y and normally distributed and it is a random variable but i found somewhere written u~N and u~... 1answer 19 views ### Distribution Theory - bivariate normal distribution Question: Let X and Y have a bivariate normal distribution with E(X) = 5, E(Y ) = −2, var(X) = 4,var(Y ) = 9, and cov(X, Y ) = −3. U and V are defined as U = 3X + 4Y and V = 5X − 6Y .Determine the ... 1answer 17 views ### 52% of people want to ban smoking Use the normal approximation to estimate that over half of a sample size$n$support the the ban 52% of people want to ban smoking. Use the normal approximation to estimate that more than half of a given sample size$n$support the the ban. q=1-0.52=0.48 For$n=11, 101, 1001$Are these steps ... 1answer 26 views ### Let$ 0 \lt \alpha \lt 1$.$z_a$is a solution to$\Phi(z_a)=\alpha $. Let$ 0 \lt \alpha \lt 1 $.$z_a$is a solution to$\Phi(z_a)=\alpha $. 1.) What is the relation between$z_a$and$z_{(1-a)}$2.) Find$z_a$(with an error that does not exceed 0.01) for the ... 2answers 31 views ### Central limit theorem on packs of variables I'm trying to solve the following exercise: Let$\mu$be a probability distribution on$\mathbb{R}$having second moment$\sigma^2<\infty$such that if$X$and$Y$are independent with law$\mu$... 3answers 50 views ### Let$X\sim N(3,4)$. Find$\mathbb{P}(X<7)$,$\mathbb{P}(X \ge 9)$Let$X \sim N(3,4)$. Find$\mathbb{P}(X\lt7)$,$\mathbb{P}(X \ge 9)$, and$\mathbb{P}(|x-3|\lt 2) $Okay lets figure out the PDF.$\mu=3$,$\sigma=4. $$f(X)= \frac{e^\left(\frac{-(x-\mu)^2}{2 \... 2answers 38 views ### Normal distribution, probability and modulus question [closed] Say X is a random variable which is normally distributed with mean 0 and variance 1. How do I find k such that$$\mathbb{P}(|X-k| < |X+k|) = 0.7$$1answer 13 views ### Normal Distrubution Question - How many components are defective and acceptable? A component is defective if oversized. A sample of 460 components produced by a machine have a mean size of 7.2 cm and a standard deviation of 0.12 cm. The maximum size of an acceptable component is 7.... 3answers 46 views ### Calculate E(X^{2n}) where X is normal (0,1) I need help proving the following: Let X be normally distributed with parameters \sigma=0 and \mu=1. Let n be a positive integer. Show that:$$E(X^{2n})=\frac{(2n)!}{2^nn!}=:(2n-1)!!I've ... 0answers 18 views ### Normal Distrubition Question - How many wires will meet specifications? Wires manufactured for use in a certain computer system are specified to have resistances between 0.12 ohm and 0.14 ohm, the actual measured resistances of the wires produced by company A have a ... 0answers 27 views ### Ratio of two normal random variables with the same mean and same standard deviation I would like to compute the probability density function of Z = \dfrac{X}{Y} with X and Y following a non-standard normal distribution with the same parameters (same mean and variance). 1answer 18 views ### GRE Quantitative problem on distributions I was doing some problems on this .Can some one please help me with the following: Here the given answer is that quantity B is grater than Quantity A. How is this obtained? Do we know anything ... 1answer 13 views ### Lognormal distribution inverse equivalent In Lognormal distribution if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Is there inverse equivalent to lognormal distribution where Y = exp(X) has a ... 0answers 39 views ### Gaussian processes and bias I would like to simulate two Gaussian processes along a time grid. Ideally, I would like to see the average of the samples, for each grid point, to be close to the mean. Using the antithetic method, I ... 1answer 74 views ### Conditional Expectation of the minimum of two identical log-normal distributions I'd like to compute the closed form mean of the minimum of two truncated log-normal distribution (on another interval than its truncation). I have: \int_{a}^{\infty} \int_{a}^{\infty} min(v, v') \ ... 1answer 43 views ### Characterization of Normal RVs by uni variate version? If X is a symmetric n-dimensional random vector with mean 0 then is it true that: \begin{align*} & X \text{ follows a multivariate normal law} \\ & \text{iff} \\ & \|X\| \text{is a ... 1answer 25 views ### Find the critical value of given statistical problem, t-distribution My solution doesn't match the one given in my course, however I can't quite see what I've done wrong. Can someone give me a heads-up? Problem Given the following: y: N(2,3) z: \chi^2(7 d.f.) ... 1answer 33 views ### bayesian posterior of truncated normal distribution with uniform prior Let N_T(\mu,\sigma) be a truncated normal distribution with support on [0,1]. Draw x \sim N_T(\mu,\sigma) (What I want to model is, I have a unknown quantity \mu \in [0,1], but I only ... 0answers 21 views ### (X_n)_{n\in\mathbb{N}} independent with standard Gaussian distribution Let (X_n)_{n\in\mathbb{N}} be a sequence of independent random variables, each with standard Gaussian distribution. For a given K>0, prove that:\lim_{n\to\infty} \frac{1}{n}\log{P\left(\... 0answers 49 views ### FindP(B_3>0,B_6>0)$where$(B_t)$is a Brownian motion Suppose that$B_{t}$is a standard Brownian Motion. What is the probability that both$B_{3}$and$B_{6}$take positive values? This is what I've tried but then I get stuck and I'm not sure how to ... 1answer 22 views ### Derivation of a property of standard Wiener processes I am reading A Standard Wiener Process and am struggling to piece together how they arrived at their conclusion. The major properties of any Wiener Process are:$W(t) = 0W(t) - W(s) \sim N(0, t-...
I have a normal distribution $N$ with $μ=U/2$ and $σ=U/12$ (an approximation of the Irwin-Hall distribution) which has been bounded and normalized to $[0,U]$. I will now repeatedly generate random ...