# normal distribution

1. ### What will be the transformation and Jacobian of transformation for the following case

Let X_i\sim N(\mu_i,\sigma^2) ; where [i=1,2,\ldots,n] show that \bar X and (X_i-\bar X) are independent. If all X_i had same mean \mu then we transform the random variables X_i; [i=1,2,\ldots,n] to Y_1=\bar X Y_2 =X_2-\bar X Y_3 = X_3-\bar X \vdots Y_n = X_n-\bar X...
2. ### Appropriate tests for comparing 2 normally distributed datasets (ttest?)

Hello, It's been a while since my A-level statistics course so I just want to make sure I'm doing the appropriate test for my data. I'm a PhD student working in X-ray crystallography. My situation is that I have 2 populations of data, of varying sizes, in one population the samples have...
3. ### Z-scores with non-normal data

Hi, I am reviewing someone's study in which they used z-scores to standardize and compare data. I see no mention of their test for normality and when I looked at their raw data, I found much of it to be heavily skewed and not-normally distributed. I need to determine whether this means...
4. ### Normally distributed RVs

Hello. I'd like to know how can I calculate the probability that normally distributed random variables locate on the surface area on a cylinder? I thought about it myself and I came to multivariate (trivariate) normal distribution.But I'm not sure. Thank you in advance
5. ### Measuring the presence of a correlation

1. Given a frequency data set (collected from 10 users by letting them watch certain videos and asking some questions about the videos) how do I determine any correlation between two variables (Correctly guessed and Correctly memorized) and calculate the significance level? Video...
6. ### Calculating the average variance of several normal distributed variables

Hi, I have the following problem. I'm trying to average several normal distributed variables. To make it more easy, I'm using z-scores. The mean of the average is (Mx1 + Mx2 + Mx3)/3, in this case 0. But how do you calculate the variance? If I assume they are independent, am I...
7. ### Plotting a normal distribution curve over a histogram

I'm trying to plot a normal distribution curve over my histogram but I can't get my code to work for the curve. It just looks like it's plotting a very low curve, what am I doing wrong? This is my code: minutes<-c(107, 116, 127, 126, 111, 90, 125, 124, 92, 121, 131, 137, 95, 101, 101, 111...
8. ### Applying Normal Distribution

So here is the question followed by what the steps I took to solve it. Please let me know if I have done this correctly: Question: The time needed to complete an exam in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes...
9. ### t test or ANOVA, ? normal distribution

I have an experiment on cancer cell lines. There are 7 cell lines. Each cell line is treated with a different concentration of the same drug. The average concentration that killed half the cells in each cell line is calculated, along with a standard deviation as follows: Cell Line //////...
10. ### distribution of ln(X) when X is binodal normal

Hi everyone. I am trying to find the distribution of ln(X) when i know that X is distributed as a binodal normal distribution, in other words: X \sim p \cdot N(a,\sigma^2) + (1-p) \cdot N(b,\sigma^2) which I suppose also can be written as X \sim N( (p, 1-p) ( a, b)^T , \sigma^2)...
11. ### Use Normal Distribution and Chi-square distribution

My question is as follows: If X and Y are independent random variables, X has a normal distribution with mean 2 and variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find "u" such that: P(X > 2 + u√(y) = .01 note: "√" stands for square root Anyway, I...
12. ### How to calculate the probability between two normal distributions?

Using the normal distribution. Let X  N(1, 2) and Y  N(2, 3) where N(μ, variance) denotes the normal distribution with mean μ and variance . X and Y are independent. Let U = 2X + 3Y . What is the mean of U? What is the variance of U? What is P(6<=U<=7.5)? What is P(X>Y)?
13. ### Confidence Intervals for Pairwise Independant Normally Distributed Samples

Good day, I have been thinking over this exercize for a couple of hours now and I have trouble finding a starting point. Suppose that X1,i iid∼ N(µ1, σ²), X2,i iid ∼ N(µ2, σ²), that the samples are pairwise independent, and that σ is known. Derive a 1 − α conﬁdence interval for µD = µ1 − µ2 I...
14. ### t-test on percentage

Hi all, Pretty simple question: I have two mean performance scores in percent, one is 70% +/- 3(SEM) and one is 95% +/- 1. Someone said I shouldn't do a t-test to compare these since data can't be normally distributed. Is that true? How would I compare these means then? thanks!
15. ### Normal distribution theoretical moments

how we can show that the follwoing equility holds E[(x-\mu)\sigma]=0 E[(x-\mu)^2\sigma^2-1]=0 E[(x-\mu)^3\sigma^3]=0 E[(x-\mu)^4\sigma^4-3]=0
16. ### Standardizing a normal variable

I am trying to understand the binomial distribution, normal distribution and standard normal distribution using the attached excel file. The example in use is calculating the distribution of a random variable X which is equal to k successful shots out of n trials in basket ball. The...
17. ### Test whether the SD of multiple normal distributions differs between two genes

Hi, I am comparing data on gene expression between two different genes that have been tagged with GFP. Gene expression is measured using flow cytometry so that gene expression is a continuous variable along the x-axis, with counts on the y-axis. For each gene I thus have a normal distribution...
18. ### area under curve normal distribution

Two issues, that I am confused about after reading statistics books. Example: weight of an adult is normally distributed with mean of 180 lbs and std dev of 20 lbs. 1) is the area under the curve equal to 100% or would the area be equal to the mean? The descriptions I see in statistics...
19. ### Combining standard deviation/normal distribution (do I have this right?)

I have a variable with a mean of 52% and a standard deviation of 2.5%. However, the 52% mean was derived from an opinion poll which itself has a 3% margin of error, which I take to imply a standard deviation of 1.53%. Assuming a normal distribution I can calculate from the former a 21% chance of...
20. ### Case control, lot of parameters, N and n-Normal dist. Which test and data expression?

Firstly, my english are not so good, sorry. I will be very happy if someone help me. I am doing a case-control study, people with and without schistosomiasis. How may I perform the Kolmogorov-Smirnov test, my groups must be together or not? I think that they must stay together. Then, I...