# Tagged Questions

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### Confidence Interval for Regression Coefficient ,$\beta$

In the book 'Applied regression Analysis' by Draper/Smith, it is written that : Obtain individual $100(1-\alpha)\%$ confidence interval for the various parameters separately from the formula ...
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### Mantel-Haenszel $\chi_1^2$ statistic

I was doing a particular example from the book Epidemiologic Research by Kleinbaum(example 15.6) and didn't understood some basic statistical aspect. ...
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### Given N-distribution, calculate expected value and Var of a function

$X_{{i}}=X_{{1}}...X_{{n}}$ is an iid. random variable with the distribution $N \left( {\frac {\alpha}{\beta}},{\frac {{\alpha}^{4}}{{\beta}^{4}}} \right)$ I would like to calculate the expectation ...
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### Find the probability that the average of X and Z is greater than Y. Where X, Z, and Y are normal RVs.

Here is the exact statement: Suppose X,Y , and Z are independent random variables. X is a normal random variable with mean 5 and variance 16, Y is a normal random variable with mean 7 and variance ...
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### Normal Distribution burnout… of lightbulbs.

Thank you for looking through this problem, much appreciated! I tried to work out the answer for a, but I got .2946 when the actual answer is .3085... How do I start this? By the way, I just want to ...
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### An IB Math HL question on normally distributed random variable.

Some Background: Tim goes to a popular restaurant that does not take any reservations for tables. It has been determined that the waiting times for a table are normally distributed with a mean of ...
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### Finding probability density function of a linear combination of mutually independent normal random variables

I'm finding the probability density function of the random variable U defined in the following manner: $$U=\frac{1}{2}(Y_1+3Y_2)$$ CORRECTION: The line above is supposed to be ...
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### moment generating function of normal distribution

I know this question relates to the chi-squared distribution, but I think what the question wants me to do is somehow derive this distribution from the information given. I have a normally ...
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### Normally distributed from 0 to 99th percentile

Assume the length of waiting at supermarket is approximately normally distributed with mean 6 minutes and standard deviation 1.5 minutes. (1) What length of the waiting time constitutes the 99th ...
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### Confidence interval and normal distribution

For question (a), is the answer 0.7143? For question (b), is the answer 10.85 and 11.95 ?
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### Probability: Normal Distribution

Each item produced by a certain manufacturer is, independently, of acceptable quality with probability $0.95$. Approximate the probability (by a normal distribution) that at most $10$ of the ...
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### Approximating Probability by Central limit theorem.

A large number of insects are expected to be attracted to a certain variety of rose plant. A commercial insecticide is advertised as being $99$% efective. Suppose $2000$ insects infest a rose ...
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### Conditionally normal distribution with a normal mean

The following question is part of my homework: Suppose that $\mu \sim N(0, 1/\alpha)$ and $x|μ \sim N(\mu, 1/\beta)$. By integrating out $\mu$, show that the marginal distribution of $x$ is given by ...
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### Calculating integral with standard normal distribution.

I have a problem to solving this, Because I think that for solving this problem, I need to calculate cdf of standard normal distribution and plug Y value and calculate. However, at the bottom I ...
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### Probability , Geometric and Gaussian

So,I'm good at the questions which require the understanding of basic formulaes , but this one my prof said needs me to think (for the first one)'geometrically'=Stumped. Please Help! The second is an ...
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### How to integrate the following formula about normal distribution

How to compute the following formula? $$\int_{-\infty}^{+\infty} \Phi(x) N(x\mid\mu,\sigma^2) \, dx$$ $$\int_{-\infty}^{+\infty} \Phi(x) N(x\mid\mu,\sigma^2) \, xdx$$ where ...
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### Calculating probability of difference of two distributions.

A has normal distribution of scores of students with $X \sim \mathcal N(625, 100)$ B has normal distribution of scores of students with $X \sim \mathcal N(600, 150)$ Now I have to calculate ...
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### What proportion are above x of sample size n where X ~ N(0,1) Homework

I have a homework question that I'm not quiet sure of. It follows as so: Consider a random variable $X$ that has a standard normal distribution with mean $\mu=0$ and standard deviation $\sigma=1$. ...
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### Given a covarince matrix, generate a Gaussian random variable

Given a $M \times  M$ desired covariance, $R$, and a desired number of sample vectors, $N$ calculate a $N \times M$ Gaussian random vector, $X$. Not really sure what to do here. You can calculate ...
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### Proving MLE for normal distribution

I need to prove that using maximum likelihood estimation on both parameters of normal distribution indeed maximises likelihood function. So, the log-likelihood function for parameters $\sigma$ and ...
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### Derivation of the density function of student t-distribution from this big integral.

My lecturer posed a question where we derive the density function of the student t-distribution from the Chi-square and Standard normal distribution. I worked on this question for days, and I am ...
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### Normal distributions with errors

I'm able to do the following problem: In a road, the speed limit is $80$ km/h. The car speeds follows normal distribution and has average $70$ km/h and standard deviation $6$ km/h. How many percent ...
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### Finding 'symmetrical range' from mean.

A machine used to make butter where its masses are normally distributed with mean m and standard deviation s.It is found that 5% from these butters are having mass more than 85g where else 10% are of ...
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### Normal distribution with absolute value

I am new to the normal distribution topic. While I have understood and solved various different kind of questions, the normal distribution questions with absolute value, are the ones I have no idea ...
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### Upper Limit in normal distribution?

(Iv already solved the a) part with the answer 0.2119, which is correct. The b) part asks for the upper limit, I dont know what an upper limit is in these type of questions. Can any one give me ...
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### Mean and standard deviation with percentages

(I am very new to this topic and I have tried many questions successfully. Except story questions like these, which confuse me. Can I just get hints that help me out instead of the answer? or like ...
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### Normal Distribution and a Discrete Amount

From what I understand about normal distribution is that you make a discrete number continuous by adding .5 which every way the question asks for. What if you were to have a discrete number with a ...
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### Distributing $m$ balls into $n$ urns with no urn left empty. [duplicate]

If $m \geq n$, how many different ways are there of distributing $m$ indistinguishable balls into $n$ distinguishable urns with no urn left empty? I have no idea how to even start with this so any ...
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### Homework Help. Probability Density Functions.

$X$ is $N(10,1)$. Find $f(x|(x-10)^2 < 4)$ This is a homework question. I can only figure out that X is normally distributed with mean 10 and variance 1. Can you please explain what is meant to ...
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### Problem involving the bivariate normal distribution

If $X$ and $Y$ have a bivariate normal distribution with $\mu(x)=\mu(y)=0$, $\rho=0$, $\sigma(x)=\sigma(y)=10$. Find the following: A) The probability of getting a point $(x,y)$ inside the ...
I've been working on review problems, and this one has me completely stumped. Let $X_1 ... X_{10}$ be a random sample from a $N(3,\sigma^2)$ distribution, where $\sigma^2$ is unknown. Using the ...
### Does $0$ correlation imply independence for marginally normal distributions?
Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$. Can someone give a hint why this is true ?