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_2 =X_2-\bar X
Y_3 = X_3-\bar X
Y_n = X_n-\bar X...
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...
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...
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
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?
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...
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...
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:
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...
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 //////...
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)...
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
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)?
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
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?
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...
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...
Two issues, that I am confused about after reading statistics books.
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...
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...
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...