Normal distribution Definition and 240 Threads

Homework Statement Z = (Z1, Z2, ... Zd) is a d-dimensional normal variable with distribution N(0, E). Let A be invertible matrix such that AA' = E. (E = sigma = covariance matrix). Find the distribution of Y = (A^-1)*Z. The Attempt at a Solution I'm pretty sure the solution is normal...

I am confused with my homework problem in which it asked "If the random variable is normal, specify its distribution". What does it want? sampahmel

Homework Statement I was asked to plot a distribution curve, but before that we had to deal with working means instead of a real mean. So the problem is :is it ok to plot a normal curve based on the standard deviation from the working mean? We were asked to compare our results with antoher...

I was wondering what owuld the outcome be if I multiply both normal distribution eg N (5, 100 ) and M ( 10,100 ) i know the operations for addition and subtraction but what if N.M what do i get ?

Homework Statement Given X and Y are independent, normal distribution variable. a and b are constants. Homework Equations The probability of P(X+Y<b,X<a) The Attempt at a Solution P(X+Y<b,X<a)=\int_{-\infty}^{a}f(x)\int_{-\infty}^{b-x}f(y)dxdy Is there a close-form solution...

A normal distribution can be completely defined by two parameters - the mean and the standard deviation. Given a normal distribution however, say X, how can I use just the mean and the standard deviation to give me conditional expected values for X<=0 and for X>0? I am guessing the distribution...

ok guys , i need an answer to this question , use both moment generating function and cummulative function to show that z=(x(bar)-\mu)/(\sigma/\sqrt{n}) if x(bar) is based on a random sample of size n from a normal(\mu,\sigma^2)

Hello This attachment is a practice paper I am doing. I know how to do everything except for questions 11, 12 and 13 so I would appreciate it if someone could please show me the process for working them out. thanks in advance.

Ok, I know this problem is below everything on this forum, but I am an English major with no math skills and I'm REALLY stuck. This question is as follows: 1)Assume that the number of items borrowed per person per year in a library is normally distributed with a mean of 87 and a standard...

Homework Statement Find Z0 such that P(z > z0) = 0.1234 Homework Equations The Attempt at a Solution Z is the mean which is 0. So if Z0 is less than the mean it should be a negative number. Looking at the table 0.1234 does not show up but the closest is 0.1217 which is 0.31. So Z0...

Homework Statement I'm having difficulty integrating something, click http://en.wikipedia.org/wiki/Normal_distribution and under Cumulative distribution function, there is an integral - how do you get to the next line? Homework Equations The Attempt at a Solution i have...

Homework Statement Given the normal distribution X_{ij} \sim N(\mu_i, \omega^2) where i = 1,2 and j = 1,...,n deduce that H_{0\mu}: \mu_1 = \mu _2 The Attempt at a Solution Do I take in the Likelyhood function here? and use it to analyse the case? Sincerely Hummingbird p.s. I have...

Let Y = a + bZ + cZ2 where Z (0,1) is a standard normal random variable. (i) Compute E[Y], E[Z], E[YZ], E[Y^2] and E[Z^2]. HINT: You will need to determine E[Z^r], r = 1, 2, 3, 4. When r = 1, 2 you should use known results. Integration by parts will help when r = 3, 4. I am struggling with the...

Need a little help here: Find the random variable coefficients y1 and y2 where P(y1 < y < y2) = 0.5. Where mean is 0.7 and standard deviation is 0.03 (not sure if you need that). I have no clue where to start with this one. Thanks for any help

Hi all First of all, I am new here but I am not new to statistics. But I need your help:smile: I do have a multivariate normal distribution: x~p(mu,sig) the vector x has to groups of variables, those that I know are below zero (x_bz), and those that I know are above zero (x_az). I am...

Homework Statement x represents values of a Normal random variable X, with parameters \mu and \sigma^2 z represents corresponding values of normal random variable Z, with parameters 0 and 1. z x -3 22 -2 34.5 1 72 3...

Homework Statement How would one show that dirac delta is the limit of the normal distribution? http://en.wikipedia.org/wiki/Dirac_delta using the definition \delta(k) = 1/(2\pi)\int_{-\infty}^{\infty}e^{ikx}dx Homework Equations The Attempt at a Solution

The "Empirical Rule" states that if your data is normally distributed, 95.45% of that data should fall within "2" standard deviations of your Mean. There doesn't appear to be any reference to sample size in the literature regarding the Empirical Rule and a Normal Distribution. By contrast...

-------------------------------------------------------------------------------- Hi, I have 2 problems I would like some help. It is about normal distribution(probability) PROBLEM 1: Extruded plastic rods are automatically cut into lenghts of 6 inches. Actual lengths are normally...

Homework Statement Plastic rods are cut into nominal length of 6 inches. Actual lengths are normally distributed about a mean of 6 inches and their standard deviation is 0.06 inch. Question: To what value does the standard deviation need to be reduced if 99% of the rods must be within...

Hello i need help on generating a normal distribution curve. I need to generate this curve in excel and put it on top of my histogram . i have already tried using normdist but nothing is happening . i am using excel in office xp and haven't got a clue please help!

Dear all, I am trying to find out a good bound on the deveation of a normal distributed variable from its mean. The noramly distributed variables X_t \sim N(\mu, \sigma^2), t= 1,2,...,n are iid. Applying the Chebyshev inequality on the mean of these n iid variables: m_n = \frac{1}{n}...

The weight of a large loaf of bread is a normal variable with mean 420g and standard deviation 30g. The weight of a small loaf is a normal variable with mean 220g and standard deviation 10g. 1) Find the probability that 5 large loaves of bread are heavier than 10 small loaves. My Working...

When solving for the variance of the normal distribution one needs to evaluate the following integral: INT(-infinfity to infinity)[x^2*e^(-x^2/2).dx] I proceed using integration by parts: [-x.e^(-x^2/2)|(infin to -infin) + INT(-infin to infin) 2*e(-x^2/2)dx] However apparently...

Hi all, I need help with a problem. The lifetimes of interactive computer chips are normally distributed with mean u = 1.4 * 10^6 hours and sigma = 3 * 10^5 hours. What is the approximate probability that a batch of 100 chips will contain at least 20 whose lifetimes are less than 1.8 *...

Normal distribution. What is the value of sigma (dispersion) for maximal probability P(1<x<2) ? Excel calculation: sigma is about 1.471. But what would be an analytical solution? http://img500.imageshack.us/img500/558/normdistrib19ql.gif

Got a question I need a little bit of help. Assume the scores on an aptitude are normally distributed with mean=500 and standard deviation=100 What is the middle 40%? My workings p(x1≤x≤x2)=p(z1≤z≤z2) => p(z1≤z≤z2)=p(z≤z2)-p(z≥z1)=p(z≤z2)-[1-p(z≤z1)] p(z≤z2)=0.7 p(z≤z1)=0.3...

Note: You'll need the Normal Distribution Table. A certain type of light bulb has a lifetime in hours which is normally distributed with mean μ=650 and standard deviation σ=40. What is the probablility that a randomly selected light bulb has a lifetime in the range (700, 850)? Now this is...

Hypothesis testing with normal distribution... I've been learning about Hypothesis testing with normal distribution, but I don't understand the need for the significance level. By this I mean that i understand that according to the Central Limit Theorem a distribution of the means will be a...

Hi Guy's, I have problems answering questions like this...(i'll just make up a question) The time it takes to bake a cake in a bakery shop is a random variable that has a normal distribution with a mean of 4.5 minutes and standard deviation of 1 minute. Lets suppose this bakery has...

the only tables that I see go from -3 to 3 in my textbooks. but I keep seeing problems on the textbooks tha ask for p( -4.5 < z < .5) how do I solve this?

How do you derive the normal distribution formula?? How was it derived? (mu=population mean, sigma=std. deviation) (see below thumbnail for formula)

so w/ the normal distribution, to find the area between 2 numbers, say P(a \leq Z \leq b), , I need to split this up into 2: P(-\infty < z \leq b) - P(-\infty < z < a). my question is, why is it not P(a < z < +\infty) ?

For my lab i have to use my data that i recorded in excel and for that into a chart. The thing is, i have no clue where to even start. The chart is supposed to have the avg at the top of the curve and the standard deviations to the left and right of the avg. On the Y-axis is supposed to be the...

Phi- normal distribution (how to look normal tables!) hello, can anyone please tell me how to look up values for the following from the "normal table" distribution. \phi^-1(0.25) ans. is -0.68 but i can't figure out how the **** it is so! so please someone reply fast 'cause this...

" A contractor has recently purchased a new bulldozer. On previous jobs, 15 out of a total of 50 bulldozers have broken down before the end of the job. What is the mean and standard deviation of the probability distribution describing the probability of failure of a bulldozer? Note...

I am looking for a mathematical equation which is similar to the Gaussian normal distribution curve, but I need one which terminates at a finite x = X and not at infinity, ie, f(x \geq X) = 0, but, f(x \leq X) = a function which has a Gaussian shape-like curve. Is there one such as this that...

Hi, I have a question If X1,X2,...,Xn are independent random variables having chi-square distribution witn v=1 and Yn=X1+X2+...+Xn, then the limiting distribution of (Yn/n) - 1 Z= --------------- as n->infinity is the standard normal distribution. sqrt(2/n)...

Given P(x)= \frac{1}{\sigma \sqrt{2\pi}} e ^ \frac { -(x - \mu )^2}{2 \sigma ^2 } This is of course the normal distribution curve. When \mu = 0 and \sigma = 1 I can integrate this from minus infinity to positive infinity no problem using polar coordinates and a bit of multivariable...

Greetings to all, I have run into some extreme difficulty with this straightforward topic. My problem is that I can’t work out which tables to use. There is the normal table and then the percentage points table. When the question states that the probably under the curve is a percentage I...