Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.
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0answers
24 views
Evaluate the right side
$X_i$ [where $i=1,2,\dots n]$ is normally distributed with mean $P$ and variance $1$, that is $X_i~N(P,1)$
then how
$$-\frac{1}{2}\sum^n_{i=1}X_i^2–\frac{1}{2}nP^2=-\frac{n}{2}P^2$$
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0answers
15 views
Probability that difference sample mean from population mean is 1.96 sd [closed]
Probability that difference sample mean from population mean is 1.96 sd
a)68%
b)95%
c)47/5%
d)99%
2
votes
2answers
21 views
Homework Question. Joint Probability Destribution.
Here is the question.
The joint PDF of X and Y is given by $f_{XY}(x,y) = {\frac 14} e^{-|x|-|y|}$. Find $P(X \le 1 ,and, Y \le 0)$
Solving the problem I first found the marginal probabilities of X ...
1
vote
1answer
18 views
manual random selection, how?
Thas a question for my test in one hour...how do I do that? I have tried to find it online but no way...any help please?
Suppose that a simple random sample of 20 of the Aucklanders surveyed is to be
...
0
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0answers
19 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 S.D.(squared) 1.
Can you please explain what is meant to ...
1
vote
0answers
23 views
Given some data, how can I tell how well it fits a (continuous) uniform distribution?
I have a set of $30$ real numbers between zero and one. Let's say that the null hypothesis is that this data set fits a uniform distribution and that the alternative hypothesis is that this data set ...
1
vote
1answer
18 views
How to combine covariance matrices?
I have a data set of points in three dimensions.
I'm calculating the barycenter (mean) and $3\times3$ covariance matrix from this data set.
I store the average, the $3\times3$ matrix (where really ...
0
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0answers
14 views
Predict binary occupancy vector from history of vectors
I have a set of binary vectors where each vector represents one day of occupancy in a house and consists of 48 elements (each element for 30 minutes of the day). Each element can be 1 meaning that ...
0
votes
0answers
21 views
How do you calculate total impact from a number of correlated events
Say that you have 10 events that each have a probability from 0% to 100% and each have a potential impact that is either 0 if the event doesn't happen or a number between $0-$10 if the event does ...
-3
votes
0answers
24 views
Variance of $\frac{1}{\bar{x}}$ [closed]
The X is distributed geometrically and so I got
$$V\left(\frac{1}{\bar{x}}\right)=\frac{n\theta^2}{(1-\theta)}$$
0
votes
0answers
17 views
Vector similarity for prediction
I have vectors of same length consisting of 1 and 0. I am trying to find out how similar they are. So far I am using hamming distance that I calculate sum of one vector then sum of second vector and ...
0
votes
2answers
23 views
densities being absolutely continuous wrt Lebesgue measure
I'm reading an article with an assumption similar to: "The density $f(.)$ exists and is absolutely continuous with respect to Lebesgue measure". I don't understand this assumption because $f$ is not ...
0
votes
0answers
17 views
2 independent normal distributions, find sample size given distribution, power and hypothesis tests
For 2 independent normal distributions N($M_1$,$\sigma$$_1^2$=400) and N($M_2$,$\sigma$$_2^2$=225). Let $\theta$=$m_1$ - $m_2$. Let $\bar X$ and $\bar Y$ be the observed means of two independent ...
2
votes
2answers
18 views
How to estimate CTR (click-through rate)?
How many times banner should be shown to estimate CTR?
For example, a banner was shown x times, and was clicked y times.
CTR = y/x;
How to evaluate incaccuracy ...
1
vote
1answer
8 views
Binomial Model Probability
Can someone explain how to solve the following stats problem:
68% of students study for an exam. Of those who study, 97% pass. Of those who do not study, 60% pass. What is the probability that a ...
