Probability or Statistics – Transformation of Random Variables and Common Distributions

Given a variable $ y_i $Normally distributed with 0 mean and $ σ_y $ standard deviation

$ y_i $ ~ Normal distribution[0[0[0[0$ σ_y $ ]

I would like to get with mathematica:

  1. The distribution of:
    $ bar {x} = frac { sum_ {i = 0} ^ ny_i} {n} $

  2. The common distribution of $ ( bar {x}, y_i) $

Thank you for your helpful comments

Math – Create levelup statistics based on curves

I'm creating a simple level-up system and want to base my statistics on curves so I can adjust them more easily. I know it's a mathematical function, but I have no idea what to look for.


I need to create this curve and get the value of every x-increment.

Enter the image description here

The engine I use is Renpy and the speech python. If you can tell me which terms you are looking for, I may be able to find something on the subject.

Statistics – What is a good approximation to the asymptotic normality?

I have conceptual doubt. Suppose I have $ X_i stackrel {iid} { sim} N ( theta ^ *, 1) $ and I know that (I have the information) $ theta ^ {*} geq 0 $, So I have the limited maximum likelihood estimation:

$$ has { theta} _ {CMLE} = max { bar {X} _n, 0 } $$

I know that when $ theta> 0 $, then

$$ sqrt {n} ( has { theta} _ {CMLE} – theta ^ {*}) to ^ {d} N (0,1) $$

I heard that when $ theta ^ {*} $ is very close to zero, then I have no good approximation. For example when $ theta ^ {*} = $ 0.00000000000000001 $, Why should not I have a good rapprochement? If I know that, though $ theta ^ {*} $ is very small, it will always be positive and my above convergence will be valid. How would this be a good rapprochement?

Statistics – help to calculate the correlation coefficient for my data

I need help if I know if I calculate the correlation coefficient correctly for my research. I have three sets of high-order factors (one score / one factor for each participant) that must be correlated with the pressure they believed to confess (rates on a scale of 1 to 10). How can this be calculated in Excel or R? Delivery of the data per picture. Enter the image description here

Instead of voting, help me.

statistics – show $ has { theta} $ = $ frac {x _ {(n)}} {3} $ is biased

The uniform distribution (0,3θ) ​​has pdf

$ f left (x right) = frac {1} {3θ} $ when $ 0 le x le 3θ $ and $ 0 $ Otherwise

from where $ θ> 0 $

To let $ x_1, …. x_n $ a random sample from this population distribution $ x _ {(n)} $ is the maximum

To let $ has { theta} $ = $ frac {x _ {(n)}} {3} $ be an estimator for θ

Show that this is biased

I know how to do that normally $ x _ {(n)} $ confuses me

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Statistics – Independent Probability Ratio Test

To let $ n $ Independent experiments of an experiment will be like this $ x_ {1}, x_ {2}, …, x_ {k} $ are the respective times at which the experiment ends in mutually exclusive and exhausting events $ A_ {1}, A_ {2}, …, A_ {k} $, If $ p_ {i} = P (A_ {i}) $ is constant throughout $ n $ Studies, then the probability of this particular series of studies $ L = p_ {1} ^ {x_ {1}} p_ {2} ^ {x_ {2}} cdot cdot cdot p_ {k} ^ {x_ {k}} $,

  1. I remember it $ p_ {1} + p_ {2} + … + p_ {k} = 1 $show that the probability ratio for testing $ H_ {0}: p_ {i} = p_ {i0}> 0 $ $ i = 1, 2, …, k $is given against all alternatives by
    $ lambda = Pi_ {i = 1} ^ {k}[frac{(p_{i0})^{x_{i}}}{(frac{x}{n})^{x_{i}}}]$
  2. Show that $ \ $
    $ -2ln lambda = Sigma_ {i = 1} ^ k frac {x_ {i} (x_ {i} – np_ {0i}) ^ 2} {(np_ {i} & 39;) ^ 2} $ from where $ p_i & # 39; $ is between $ p_ {0i} $ and $ x_ {i} / n $, Note Expand $ ln p_ {i0} $ involved in a Taylor series with the rest in the term $ (p_ {i0} – x_ {i} / n) ^ 2 $,
  3. For big $ n $argue that $ x_ {i} / (np_ {i} & # 39;) ^ 2 $ is approximated by $ 1 / (np_ {i0}) $ and thus -2ln$ lambda = Sigma_ {i = 1} ^ {k} frac {x_ {i} (x_ {i} -np_ {0i}) ^ 2} {(np_ {i} & 39;) ^ 2} $

I am not sure if it is a Bernoulli, i.
$ f (x; n, p) = C ^ {n} _ {x} p ^ {x} (1-p) ^ {n-x} $, To let $ omega = { {p_i: p_i = p_ {i0} }} $, so $ H_0: p_ {i} in omega $, then

$ L ( omega) = Pi_ {i = 1} ^ {k} C_ {x_ {i}} ^ np_ {i0} ^ {x_ {i}} (1-p_ {i0}) ^ {n-x_ {i}} $

$ L ( Omega) = Pi_ {i = 1} ^ {k} C_ {x_ {i}} ^ np_ {i} ^ {x_ {i}} (1-p_ {i}) ^ {n-x_ {i}} $
from where,

$ lambda = frac {L ( omega)} {L ( omega)} $, then

We know that, $ has {p_ {i}} = frac {x_ {i}} {n} in $argmax $ {L ( omega)} $ $ forall i $, so

$ L ( has { omega}) = Pi_ {i = 1} ^ {k} C_ {x_ {i}} ^ n ( frac {x_ {i}} {n}) ^ {x_ {i} } (1- frac {x_ {i}} {n}) ^ {n-x_ {i}} $then the cocient

$ frac {L ( has { omega})} {L ( has { omega})} = Pi_ {i = 1} ^ {k} left[frac{p_{i0}}{left(frac{x_{i}}{n}right)}right]^ {x_ {i}} left ( frac {1-p_ {i0}} {1- frac {x_ {i}} {n}} right) ^ {n-x_ {i}} $

I am not sure that this is the right way to start

Excel – Generate fast statistics

Above all, I am new here and have learned a lot by reading.
Thanks for the great community here.

Now to my question, I have not found anything I'm looking for.
Probably because I have no idea how I could best call it … So if there is a post, I'm sorry to have a new thread open.

I have received a main sheet, 4 columns named "Round1" to 4.
The rows are specific stations like "kitchen".
I have a submarine that puts in each station / round certain names, if they can and did not do it today, all by accident.

The side panel is that there can be a maximum of 30 names and stations, but both are flexible.

Now I want to create a statistics sheet.
I've given each station over the 4 column names so I can reach the range quickly no matter where they sit.

I want that on a statistic sheet, it documents how often a particular person does a station. A sub deletes the sheet if there is a new day, and before that the statistics should be built up.

The simplest way I can think, something like this:

& # 39; & # 39; & # 39;
If Range ("StationRound1-4") = "Name" Then
Cells (statistics) .Value = Cells (statistics) .Value + 1
Otherwise end if
& # 39; & # 39; & # 39;

But I have 2 problems with it.
1. If the name exists more than once in the station because a handcrafted entry exists, it counts only 1 for statistics
2. For possible 30 stations and 30 names, I would need 150 if statements in a single sub.

Does anyone have a specific idea how to best handle this?
With an explanation that would be great.

Thanks for the help and apology for the bad english …

Probability or Statistics – All possible A of Ax = b with restrictions for A

I have a linear problem that I want to solve, but the method is quite different from the normal one. The problem is still Ax = b. However,
At this moment, I have A as unknown, except that every entry in A can only be zero or one. Further, x is known and fixed, the same is true for b.

My question, is it a simple way to make mathematica spit out all possible A-values ​​so that Ax = b is set to A.

I've tried to do a bunch of for loops, and so on, but I gave up after hours, expecting my effort to be wrong.

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