0
votes
1answer
21 views

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 ...
0
votes
1answer
29 views

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. ...
0
votes
2answers
32 views

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 ...
0
votes
1answer
40 views

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 ...
2
votes
1answer
23 views

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 ...
0
votes
1answer
22 views

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 ...
0
votes
1answer
35 views

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 ...
1
vote
1answer
36 views

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 ...
1
vote
2answers
48 views

Bivariate normal distribution question

If I have $(X,Y)$ with joint density $f(x,y)$ and $A$ is an invertible $2\times 2$ matrix, then for the random vector $(W,V)$ defined by: $$ \begin{pmatrix} W\\ V \\ ...
0
votes
1answer
27 views

P-P plot and Q-Q plot

How to draw P-P plot and Q-Q plot manually ? I have looked at different site and they explained in various way, such as one said for p-p plot in X-axis there is residual in ascending order and in ...
0
votes
0answers
7 views

Upper 5% value of distribution of the mean

The density function of a random variable x is $f(x)=ke^{-2x^{2}+10x}$. Find the upper 5% point of the distribution of the means of the random sample of size 25 from the above population. I need ...
0
votes
1answer
51 views

Bringing a density in a normal distribution form

Because I do not want to exaggerate this thread Show that $E(Y\mid X=x)$ is a linear function in $x$ I continue my special problem here. In order to make the setting clear I'll give some information. ...
0
votes
1answer
41 views

probability, normal distribution mean [closed]

Should I use a certain table for this question or should I use a special formula. A random value has a normal distribution with the mean 102.9 and the standard deviation 4.7. What are the ...
0
votes
1answer
77 views

Probability of the sum of independent standard normal random variables

Let $X_1, X_2, X_3, X_4$ be independent standard normal random variables and $$Y = X_1^2 + X_2^2 + X_3^2 + X_4^2$$ Find the probability that $Y \leq 3$. For this problem I know that the ...
1
vote
1answer
55 views

Integration of standard multivariate normal distribution

We should express the integral $I_{n}=\int_{\mathbb{R}^{n}}\exp\left(\frac{-\left\Vert x\right\Vert ^{2}}{2}\right)\mathrm{d}x$ using $I_1$. Where $\left\Vert x\right\Vert =\left(x_{1}^{2}+\cdots ...
0
votes
2answers
45 views

Normal Distribution Problem

The time taken for a computer to connect to a server is normally distributed with a mean value given by 3.3 seconds and a standard deviation of 0.66 seconds. (a) A computer is said to have a fast ...
0
votes
0answers
59 views

Finding the Probability Limit and Asymptotic Distribution of Xbar-LogYbar

I'm kinda still new to Large Sample Theory and I have already attempted the question. Not sure if I did it right. Based on Kinchin , I know Xbar converges in probability to mu and Ybar converges in ...
1
vote
1answer
47 views

Normal distribution percentile calculation

I'm working out the following problem and there is a part that I am not understanding clearly. The weight distribution of parcels sent is normal with mean value $12$ lbs and standard deviation ...
1
vote
1answer
20 views

Calculating number on normal distribution curve

Can someone please let me know if I have this question correct: ...
0
votes
1answer
59 views

Normal Distribution

Would greatly appreciate any help on this homework question, I will post my answers to parts a) and b) underneath as well but I don't think they are correct.Thanks! a) Take 10 different samples of ...
0
votes
0answers
6 views

How Do I Determine Significant Skew?

How do I determine whether a skew is significant or not? I define a significant skew as one greater than 2 x sqrt(6/N) Brown, J. D. (1996). Testing in language programs. Upper Saddle River, NJ: ...
2
votes
2answers
39 views

Distribution of $U=\frac{X}{\| X \|}$ and $R^2 = \| X \|^2$ where $X=(X_1, \dots , X_n)$, $X_1, \dots, X_n \sim$ N(0,1) i.i.d. Independence?

I have the following problem: Let $X=(X_1, \dots , X_n)$, $X_1, \dots, X_n \sim N(0,1)$ i.i.d. What is the distribution of $U=\frac{X}{\| X \|}$ and $R^2 = \| X \|^2$. Are $U$ and $R^2$ independent? ...
0
votes
1answer
61 views

Using Chi-Square to test normality.

This is a sample question we received. I can't really figure out how to statistically show that this data is normally distributed. We are to used the chi-square method and these are the steps we are ...
0
votes
2answers
60 views

Random variables in normal distribution

Suppose that $X_1$, $X_2$ are independent $\mathcal{N}(0,4)$ random variables. Compute $P\left(X_1^2<36.84-X_2^2\right)$. I have no idea how to start this. Do I have to do anything to the ...
1
vote
0answers
41 views

conditional expectation of squared standard normal

Let $A,B$ independent standard normals. What is $E(A^2|A+B)$? Is the following ok? $A,B$ iid and hence $(A^2,A+B),(B^2,A+B)$ iid. Therefore we have $\int_M A^2 dP = \int_M B^2 dP$ for every ...
0
votes
1answer
133 views

How to calculate the a Probability with Z-Score.

I have a $ \mu = -1 $ and $ \theta = 6 $. I am supposed to find the probability $P(5 < X < 11)$. My Attempt: $$P(5< X < 11) $$ $$P(\frac{5--1}{6} < \frac{X--1}{6} < ...
1
vote
1answer
97 views

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 ...
1
vote
1answer
34 views

Confidence interval and normal distribution

For question (a), is the answer 0.7143? For question (b), is the answer 10.85 and 11.95 ?
1
vote
1answer
306 views

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 ...
0
votes
1answer
54 views

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 ...
0
votes
0answers
41 views

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 ...
1
vote
2answers
89 views

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 ...
1
vote
1answer
36 views

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 ...
2
votes
0answers
94 views

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 ...
2
votes
1answer
30 views

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 ...
1
vote
1answer
104 views

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 $\sigma=1$. ...
2
votes
1answer
76 views

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 ...
1
vote
1answer
43 views

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 ...
7
votes
3answers
2k views

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 ...
1
vote
1answer
28 views

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 ...
1
vote
1answer
77 views

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 ...
1
vote
1answer
2k views

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 ...
1
vote
2answers
113 views

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 ...
2
votes
2answers
44 views

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 ...
1
vote
1answer
42 views

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 ...
2
votes
2answers
303 views

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 ...
0
votes
1answer
52 views

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 ...
1
vote
0answers
108 views

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 ...
1
vote
0answers
200 views

Hypothesis testing of normal distribution, known mean unknown variance

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 ...
1
vote
1answer
95 views

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 ?