Tagged Questions
-1
votes
0answers
47 views
This game consists of rolling two dice, one 8-sided and one 12-sided. you will roll the dice 10 times to complete the game
This game consists of rolling two dice, one 8-sided and one 12 sided. You will roll the dice 10 times to complete the game. Each roll is considered a win, if you roll a total of 6 or less. ...
0
votes
0answers
36 views
Find the moment generating function
Find the moment generating function of $W$, when $W=X+2Y+4Z$. $~X,~Y,~Z$ are independent normal distributions $\mathcal N(1,4),~ \mathcal N(2,9) \text{ and }\mathcal N(3,16)$.
0
votes
2answers
62 views
Simple homework question about normally distributed variables
The question states:
Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is
normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$.
What is ...
1
vote
1answer
34 views
How to correctly model noise?
Assume a linear mixing model $x = As$, where $x = (x_{0}, ..., x_{n})^T$ are linear mixtures of $s = (s_{0}, ..., s_{n})^T$, and $A$ is the mixing matrix.
Now, if I introduce additive noise to this ...
0
votes
0answers
34 views
Is a multivariate normal restricted to an affine set normal? [duplicate]
This seems like a basic question, but I've been confused about it anyway.
Let $X$ be a multivariate normal random variable in $\mathbb R^n$. Let $A$ be the affine set $\{x\in\mathbb R^n : ...
1
vote
1answer
50 views
Use the Central Limit Theorem to calculate the approx probabilities of Gamma RVs?
If $X_i, i=1,...,$ are independent, identically distributed $\operatorname{N}(0,1)$ random variables, and $Y_i = X_i^2$ are independent $\operatorname{Gamma}(\frac{1}{2},\frac{1}{2})$ RVs, use the ...
0
votes
0answers
51 views
How to compute probabilities of normally distributed variables?
Let $X_1, X_2, \ldots, X_{16}$ be independent with $N(3,4)$ distributions and $\bar{X}$ denote the sample mean. Find:
$P(-8 < 2 \bar{X} < -4)$.
A number $K$ such that $P(-K < 2 \bar{X} ...
0
votes
1answer
38 views
Questions about the sampling distribution of the sample mean
(a) Let $X_1,X_2,\cdots,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$.
Show that
$E[\bar{X}]=\mu$ and $V[\bar{X}]=\frac{\sigma^2}{n}$
What is the ...
1
vote
1answer
222 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 ...
0
votes
2answers
69 views
Normal approximation to binomial
What do I do when the normal approximation is not valid?
Here's the question I'm trying to answer:
A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
0
votes
3answers
89 views
Find the normal probability $P(|X|<1)$ using z values?
If I have a random variable that follows a normal distribution i.e.
$X \sim N(-3,4)$
and I want to calculate $P(|X| <1)$ how would I go about doing so, using the z values? Seeing as it's the ...
2
votes
1answer
80 views
Difference between the two normal distributions
I have two random variables $X$ and $Y$ which follows Normal distribution , whose pdf's are given by
$f(x)= \frac{1}{2 \sqrt{2 \pi} \sigma}[e^{\frac{-(x-1)^2}{2 \sigma^2}}+e^{\frac{-(x+1)^2}{2 ...
-1
votes
1answer
147 views
Calculating conditional probabilities given a bivariate gaussian
This is a continuation of my previous question.
I have two classes, $C_1$ and $C_2$.
$C_1$ is a bivariate Gaussian with mean $\mu = (0,0)$ and covariance $\Sigma = I$
$C_2$ is a bivariate ...
1
vote
0answers
132 views
Finding the UMVUE of the variance of a gaussian with mean zero
Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
0
votes
1answer
131 views
Covariance of a bivariate Gaussian given identity matrix
I have a homework problem about finding an optimal decision boundary. I know the formula (not really the process) for calculating one, so that may be another question entirely, but I do know I need ...
0
votes
0answers
49 views
Normal Distribution [duplicate]
Using the normal distribution. Let $X\sim \mathcal{N}(1, 2)$ and $Y\sim \mathcal{N}(2, 3)$ where $\mathcal{N}(μ, \sigma^2$)
denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. X ...
0
votes
1answer
234 views
Finding the z score and p-value of a binomial distribution
Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
0
votes
2answers
109 views
Why doesn't this represent a normal approximation to the binomial?
Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
2
votes
1answer
326 views
probability of one random variable being greater than another
Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.
...
1
vote
1answer
56 views
Approximate distribution of normal squared
I am studying for a test, one section of which will cover the delta method. This problem came from that section:
Let $X\sim N(\mu,n^{-1})$. Find an approximate distribution of $X^2$. (It also asks ...
2
votes
2answers
70 views
0
votes
1answer
101 views
How can I test the difference between a population proportion and sample proportion?
A report says that 82% of British Columbians over the age of $25$ are high school graduates. A survey of randomly selected residents of a certain city included $1290$ who were over the age of $25$, ...
0
votes
0answers
61 views
combine two Normal Dists, with one the mean of the other
For an assignment, I need to find $E_{y|\theta} [- \frac{\partial^2}{\partial^2\theta} \ln[P(y|\theta)] ]$, where $y \sim \mathcal{N}(\theta, 1)$ and $\theta \sim \mathcal{N}(0, \delta^2)$.
I can ...
1
vote
1answer
43 views
Approximating binomial distribution by normal distribution
I got a very small probability in my homework so are there any mistakes?
Benford's law says that if we have a collection of numbers, the first digit has the distribution ...
0
votes
1answer
64 views
Find the distribution of w
Suppose that X = N(0,1) and Y = N(1,1), and assume that X and Y are independent.
Determine the distribution of W = X - 2Y .
0
votes
1answer
93 views
How to find the joint density of 3 normal variables?
Suppose $U, W, V, S$ are four independent normal random variables with mean $0$ and variance $1$. Let $X=W+U$, $Y=2W+S$, $Z=3W+V$. What is $f(X, Y, Z)$?
Thanks!
1
vote
1answer
95 views
Problem on Normal Distribution
My homework problem is as follows: I start with a string of 0's of length $n$. Then, with probability $p$, I change each bit to 1 identically and independently. After that, I count the number of 1's ...
2
votes
1answer
122 views
Product of Independent Gaussian Variables
Let $X$ and $Y$ be two independent normal distributions according to $X\sim\mathcal{N}(0,P)$ and $Y\sim\mathcal{N}(0,Q)$. Is it true to say the following ?
...
2
votes
1answer
149 views
Probability error - binary message
Please, I need some support (not solution) and input to know if the way is right to go on.
Consider the communication of binary messages in a transmission medium. Any message sent is selected from ...
0
votes
3answers
690 views
Standard deviation of the sum of two normally distributed random variables
$X\sim N(52,6)$, $Y\sim (40,8)$. What's the standard deviation of $Z=X+Y$?
I'm considering to transform the linear relationship to matrix form
$$Z=\begin{pmatrix}
1& 1\\
...
2
votes
1answer
188 views
Obtaining the covariance matrix of a Gaussian random vector
I'm looking for some advice about a problem I've been assigned to solve. This is the problem. Suppose a car has to travel from P1 to P4, with intermediate points P2, P3. Say $X1$ is a r.v. that ...
1
vote
3answers
262 views
Given a normal distribution, a mean, and standard deviation what is the probability a Variable is in a range [duplicate]
Possible Duplicate:
Normal distribution probability
Issues getting to the bottom of a HW problem, but I am not looking for the answer, just some guidance.
x has a normal distribution with
...
0
votes
1answer
40 views
Probability of an event occuring [duplicate]
Possible Duplicate:
How to find percentiles of a Normal distribution?
The weight of a given Africander breed is said to follow a normal distribution with mean 200 kg and standard deviation ...
4
votes
3answers
257 views
How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
Let $X_1,X_2,\cdots ,X_j \cdots $ be i.i.d. $\mathcal N(0, 1)$ random variables. Show that
for any $a > 0$, $$\lim_{n\to \infty}P\left( \sum_{i=1}^n X_i^2\leq a\right)=0$$
It is clear that ...
0
votes
1answer
872 views
0
votes
0answers
129 views
Parameter estimation from a Normal distribution
Please can you check if am I correct?
I have a random variable $X$ normally distributed with mean $\mu$ and variance $\sigma^2$.
I generate two independent sample $T_1$ and $T_2$ with $T_1 < T_2$ ...
4
votes
1answer
2k views
How to take derivative of multivariate normal density?
Say I have multivariate normal $N(\mu, \Sigma)$ density. I want to get the second (partial) derivative w.r.t. $\mu$. Not sure how to take derivative of a matrix.
Wiki says take the derivative ...
1
vote
2answers
227 views
Combination of two Gaussians
Very close to: Finding the Bayesian classifier for a bivariate Gaussian distribution
Can somebody tell me the joint Gaussian of the following two Gaussians
(in which $C_j = C_1 \text{ or } ...
0
votes
1answer
597 views
Mean of a product of Gaussians
If I have two normally distributed random variables, X and Y, and I want to find the mean of the distribution that results from multiplying them together, which of the following two formulas should I ...
4
votes
2answers
251 views
How to determine the marginal pdf, the posterior?
How to get the marginal pdf of $p(y)$? Do you just integrate out $p({\sigma}^{2})$?
Say, the following joint distribution for $y \in {{R}^{d}}$ and ${{\sigma }^{2}}\in {{R}^{d}}$
IG: means inverse ...
7
votes
4answers
634 views
Should I use a binomial cdf or a normal cdf when flipping coins?
A coin needs to be tested for fairness. 30 heads come up after 50 flips. Assuming the coin is fair, what is the probability that you would get at least 30 heads in 50 flips?
The right way to do ...
-3
votes
1answer
84 views
Stat Qs on Mean [closed]
A manufacturing company makes windows for use in commercial buildings. The standards for glass
thickness call for the glass to average 0.375 inches with a standard deviation of 0.049 inches. A random ...
0
votes
1answer
147 views
How to compute mean vector and covariance matrix of equal distributions?
This question is an extended version of this one.
As you can see here, two distributions are equal, I need to compute the parameters a,b,c,d and e. Could you show me a way to do that?
Assume a ...
0
votes
1answer
196 views
What does “equal a priori class probabilities” mean?
I am trying to solve a problem about my homework. The problem says that
Assume a two-class problem with equal a priori class probabilities
Does it mean, mean vectors and covariance matrices ...
0
votes
2answers
1k views
What is the distribution of the sum of independent normal variables?
Just need to check the answer for the following question:
Question
Suppose $X$ and $Y$ are two independent standard normal variables:
$X$ ~ $N(0,1)$
$Y$ ~ $N(0,1)$
What is the distribution of $X + ...
5
votes
1answer
628 views
Probability of mean of random sample being in a certain range
I got this question on a test:
The average jumping distance for males between the ages of 20 to
30 is 6.5 feet with a standard deviation of 0.523 feet. What is the
probability, from a sample ...
1
vote
2answers
317 views
How to calculate the probability that the maximum of two independent standard normal distributions is greater than zero?
The R command hist(pmax(rnorm(10),rnorm(10))) gives a histogram of random variable Y, where Y is the maximum observation of two independent Gaussians.
How can I ...
2
votes
1answer
601 views
Some exercises related to sampling and the normal distribution
Following cardiac surgery, patients are encouraged to exercise regularly (assume that regular exercise is defined as exercising on 3 or more days per week). A physician suspects that patients exercise ...
3
votes
2answers
652 views
How to find a marginal distribution from a joint distribution?
So I have this joint dist
$$f(x,y) = \frac{1}{2\pi}\exp(-\frac{x^2}{2} - \frac{y^2}{2} + x^2y - \frac{x^4}{2})$$
I'd like to find $f_x(x)$. So I know that means I need to integrate function wrt y. ...
3
votes
2answers
138 views
What is the relation between two IIN mean zero random variables?
I have trouble proving the following fact in my econometrics homework. The lecturer said that I should merely look at my statistics books, but I cannot seem to find it anywhere! Thus, sorry if it is ...
