Normal distribution Definition and 240 Threads

Homework Statement So the question is, given a set of random numbers, find the mean and the value that will be >= 99% of the occurances. So for a set of random numbers between say, 1-100, if the mean is 50, how do I find out what number will be >= 99% of all observations of the time...

I'm programming a process that runs in iterations with a probability of stopping at every iteration. As it gets closer to the desired run-time, this probability should increase so that if the process is run many times over, the runtimes will form a normal distribution, with most of them having...

Homework Statement I've attached the question. Homework Equations μ=np and σ=√(np(1-p)) Im using the normal distribution function on my calculator to avoid using z tables The Attempt at a Solution The mean I calculated it to be 160/4 = 40. standard deviation...

Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.

For a normal distribution with E[x]=0 and Var(X)=1, how do we determine the Z-value of a particular percentage ? i.e. if the percentage is 5%, how do we know that Z(5%)= 1.645 ? is there a calculation involved or do we get it from observing the x-axis of the normal distribution ?

Suppose we have a normal distribution and a sample of n values from the normal distribution. To estimate the variance we can use the standard sample variance formula ( average squared distance from the mean divided by either n ( biased estimator ) or n-1 ( unbiased estimator ) ). There is...

Homework Statement Let X1,X2 be a random sample of size 2, from a normal distribution with mean μ and σ2=1. Let T=t(X1,X2)=X1+X2 be the estimator of μ and l(t;μ)=t-μ be the loss function. Compute risk function R(μ). Homework Equations R(μ)=∫∫(l(t;μ))∏f(xi;μ)dxi The Attempt at a...

Homework Statement Given X,Y RV both have normal distribution with: μ_{x}=6,μ_{y}=4,σ_{x}=1,σ_{y}=5,ρ=0.1 a. are X,Y independent? b. find P(X≤5) c. find P(Y≤5|X=5) 2. The attempt at a solutiona. no -> ρ=0.1 -> cov(X,Y)≠0 b. define Z=\frac{X-6}{1} ; Z~N(0,1) so P(X≤5) = P(Z≤-1) = \Phi(-1)...

Given a bivariate gaussian distribution, I'm attempting to find the probability p for which the ellipse of all points (x,y) for which P(X = x, Y= y) = p contains a given % of the samples drawn from the distribution. I want the 2d equivalent for the 1 dimensional case: given a normal...

Homework Statement Let Z follow a standard normal distribution. Compute E(Z^3) and E(Z^4) Homework Equations I know that mu is 0 and sigma is 1. And f(z) = e^(-z^2/2)/sqrt(2pi) The Attempt at a Solution I tried to take the integral of ∫Z^3 * f(z) from the integral from -∞ to ∞...

Hi - I have a quick question. I understand that the sum of two normal distributions is a normal distribution. Now let's say I have the z-score from one normal distribution and the z-score of another set of data that is also normally distributed and a third and a fourth etc. I just want...

Show that if X is a normally distributed random variable with parameters mu and σ2, then then show that for each real number x we have: фX(x)=ф[(x-m)/σ] I have really hard time. Any possible hint is greatly appreciated.

Quick question on bivariate normal distribution please: I know for a bivariate normal distribution, the two variables are marginally normal and all the conditional distributions are also normal. Is the reverse true? i.e. if you have two random variables that are marginally normal...

I have to compare measurements in a normal distribution with a theoretical gauss curve on "probability paper" (the y-axis has percent). Does anyone know any online guide/ information? thanks, have wasted the last three hours on this

Sorry because I have asked this other times but still not getting a reasonable answer: For bus headway times why in several articles they make assumption of normal distribution?? Generally inter-arrival times are modeled using exponential distribution but in some papers...

Homework Statement In math 334 one semester, the average student made 1200 computations per month with a standard deviation of 150 computations. Assume that the number of computations is approximated by a normal curve. Find the percent of students making between 1200 and 1600 computations a...

Homework Statement A company pays its employees an average wage of $3.25 an hour with a standard deviation of sixty cents. If the wages are approximately normally distributed, determine the minimum wage of the employees who are paid the highest 5%. Homework Equations z=(x-μ)/σ The Attempt...

Hi everybody. For sake of work I have to make an assumption that service time for patients is normally distributed. Normally the doctor has to wait one patient every half hour but anyway this time can vary being less or more. My teacher wants some theory arguments (normal distribution...

A woollen mill produces scarves. The mill has several machines each operated by a different person. Jane has recently started working at the mill and the supervisor wishes to check the lengths of the scarves Jane is producing. A random sample of 20 scarves is taken and the length, x cm, of each...

Homework Statement http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s05_qp_6.pdf question no. 6 part ii (Safety regulations state that the pressures must be between 1.9 − b bars and 1.9 + b bars. It is known that 80% of tyres are within...

Homework Statement Homework Equations The Attempt at a Solution

TITLE: Normal distributions (sorry) Question 1: Working: Now the answer for sigma i got correct, but μ i got incorrect for some reason. Could anyone explain where I've gone wrong for μ? Question 2: Workings: All i need help is with part c and d: for c) i done 1 - 0.6463 to get the...

Normal distribution modified by "potential" For a random process the distribution if described by a gaussian distribution. But if the process has components that throw off the normal distribution, can any distribution be described by a gaussian distribution with another function, call it a...

Homework Statement If I have a time series model x_1 = my + epsilon_1 x_i = my + a(x_{i-1} - my) + epsilon_i epsilon_i are iid standard normal. Can I then say that y = a_1 x_1+a_2 x_2 + ... a_n x_n is multi normal? The Attempt at a Solution All the x-es are normal...

Hi I have a set of observed data from time intervals like 4,5,... I want to fit this data to normal distribution. Is there any normalization process I can make to change them from integers to real numbers as long as normal distribution is continuous? Regards

Homework Statement Given a bivariate normal distribution with E(x1)=4 and E(x2) = 6 and Var(X) = [3 2.5] [2.5 7] Find P(2*x1>x2) Homework Equations The cdf of this bivariate...

Astrological "evidence" produced by looking at the tails of a normal distribution I just ran across this on a large news aggregation website, so I'm sure some people here might have seen it as well. http://www.inquisitr.com/173752/jail-time-predetermined-by-astrology-signs-says-police-study/...

Hi. I need some arguments to move forward the hypothesis that my data are normally distributed. Except fact that I build histogram and it is similar of shape as normal distribution how can I find some other math arguments (I mean interpreting the logic of normal distribution) to argue about...

Homework Statement A Normally distributed random variable with mean μ has a probability density function given by _ρ_...*...((-ρ2(x-μ)2)/2δ) √2∏δ|...e^ Homework Equations Its standard deviation is given by: A)ρ2/δ B)δ/ρ C)√δ|/ρ D)ρ/√δ| E)√δ|/2ρ The Attempt at a Solution...

I would like to know how to calculate the probability that a normal distribution generated a sample. More specifically, I am clustering lines so I have several assumed normal distributions. Each cluster has a mean and variance/StdDev. of both slope and length. Given a set of clusters...

Hello all, While studying for exam I came across this practise problem which is giving me some trouble. The amount , A, of wine in a bottle ~ N(1.05L, .0004L2). a)The bottle is labelled as containing 1L. What is the probability a bottle contains less than 1L? b) Casks are available...

Suppose X is the standard normal variable. is it possible to find P(X>x)? i.e does the function have a defined integral? How would you show that it is or is not defined? What information can we obtain about P(X>x).

Let's say I have a very large number of objects with some property which is Normally distributed. If I choose a subset of these objects randomly, will those objects have the property Normally distributed too? If the answer is yes, can it be proven? Thanks

Hi, I am confused with the results of a seemingly simple simulation that is generating a log normally distributed output. Please see the attached results file. Simulation: I have built a Scratch program that randomly picks six letters from a group of six letters (A, B, C, D, E & E). The...

Homework Statement The diameter of a shaft in an optical storage drive is normally distributed N(μ,σ2). The drive specifies that the shaft be 0.2500 ± 0.0015 in. Suppose μ= 0.2508 in and σ = 0.0005 in. What fraction of shafts conform to the design specifications? The Attempt at a...

Homework Statement A certain industrial process yields a large number of steel cylinders whose lengths are approximately normally distributed with a mean of 3.25 in. and a variance of 0.008 in2. If two cylinders are chosen at random and placed end to end, what is the probability that their...

Homework Statement You have 7 apples whose weight (in gram) is independent of each other and normally distributed, N(\mu= 150, \sigma2 = 202). You also have a cabbage whose weight is independent of the apples and N(1000, 502) What is the probability that the seven apples will weigh more...

Hi everyone! I have a question on how to compare two distributions. I'm currently a 2nd year biology grad student, and I'm trying to compare a parameter that evaluates the efficacy of a cell type. The math problem is this: Let X and Y each be an average of three variables divided by an average...

Homework Statement If we were to have two normal distributions, say X and Y, which are the scores of students on a test or something, a is the score of a student from X and b is the score of a student from Y, what is the probability that a randomly selected student from X will score more...

Hi, it will be a very silly question, excuse me please. I am wondering whether 3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) is still a normal distribution please? where mean is 0, delta^2 is the variance. Thank you very very much. Also, how to understand this related to...

Homework Statement A company specifies that the actual contents of packages shall not be less, on average, than the Nominal Quantity (Qn) and that not more than 2.5% of packages may be Non-Standard (NS), i.e. deviate from Qn by more than "total negative error" (TNE). Thus, if Qn=230g and...

Hello experts, Thanks to discussions with Stephen Tashi for getting me this far. See the problem statement in the attached PDF page 1. I need help solving for Qc in equation form, as a function of the other variables (N and C), preferably using erfc so I can program an accurate algorithm...

Homework Statement The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 75000 miles and a standard deviation of 5000 miles. A. What is the probability...

Homework Statement Suppose that X is normally distributed with mean 95 and standard deviation 17. A. What is the probability that is greater than 126.79? B. What value of X does only the top 16% exceed? Homework Equations z= (X-(mean of x))/standard deviation The...

Homework Statement We have Vx,Vy following a Normal standardized distribution from which we construct the following correlated variables: X, Y. We consider the events such that x(belong to)A, with 0 < Pr[x(belong to) A] <1. We want to compute V(Y|X E A), Cov(X,Y|X E A) in order to compute...

Homework Statement Hi I need a clarification before my S2 exam on Thursday. How do I find a value of P(Z<0.7925)? This is bearing mind that all the table values are to 2 decimal places. Thanks. Homework Equations Normal Distribution Tables The Attempt at a Solution...

Homework Statement In a photographic process, the developing time of prints may be looked upon as a random variable which is normally distributed with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take anywhere from 16.00 to 16.50 seconds...

I've been given the question: In a photographic process, the developing time of prints may be looked upon as a random variable which is normally distributed with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take anywhere from 16.00 to 16.50...

Homework Statement Students of a US university have an average SAT score of 600 and a standard deviation of 75. Assume the scores are distributed as a normal distribution. If X is the score of a randomly selected student, derive the expectation and variance of the mean score, Y, of n...

Homework Statement You have i.i.d. random variables X1,...,Xn ~ Normal (\Theta,c^2*\Theta^2), where "c" is a known positive constant (relative variability = std. dev(X)/E[X]) and \Theta is an unknown positive constant. Find the first four moments. E.g E[Xj] where j=1,2,3,4.Homework EquationsThe...