probability distributions – What generative model produces a scale-free network with a specific gamma?

So, what I'm trying to do is to rewire a randomly directed graph (especially a Boolean lattice) so that the lower degree distribution is scaleless. However, I need a generative model that allows me to specify $ gamma $ in $ P (k) sim k ^ {- gamma} $.

I imagine that there is a certain ratio of rewiring $ n / m $ (rewiring $ n $ out of $ m $ total edges) with preferential attachment (proportional to the existing outer degree) that will produce this result on average. But I do not know how to convert $ gamma $ in this report.

I would like to know if such a generative model exists. What would be even better is to learn how to arrive at such a model, whether it exists or not.

Probability Statistics – Approximate Probability That # Minor Students in English

The percentage of arts students (other than visual arts and music students) who write a minor in English is 20%. If 300 students are selected, what is the approximate probability that:

I. over 150 take a minor in English?

ii. between 20 and 60 years old take a minor in English?

iii. exactly 50 take a minor in English?

I've already asked this question before, but the person who answered me indicated i) 0, ii) 0.50 and iii) 0.0203. They did not provide any steps and, no matter what I tried, I could not understand how they were getting these values. I would really appreciate if anyone could explain how to get those values?

calculation distribution difficult in probability

let $ theta sim U (0.2 pi) $, $ phi = arccot ​​ frac {cos theta + h} {sin theta} $, $ 0 <h leq $ 1, please show evidence $ phi sim U (0, pi) $.

Marginalization of the transformed probability distribution

Suppose we have a probability distribution $ P (x_1, x_2) $ and its transformation $ frac {1} {C} P ^ 2 (x_1, x_2) $. Is the following valid:

$$
int_ infty ^ infty frac {1} {C} P ^ 2 (x_1, x_2) dx_2 = frac {1} {C_2} P ^ 2 (x_1)
$$

with another appropriate standardization constant $ C_2 $?

Find the probability $ P {X_1

Let $ X_1, X_2 $ and $ X_3 $ three independent random variables with pdf and cdf
$ f_ {X_i} (x_i) $ and $ F_ {X_i} (x_i) $ receptively.
Using CDFs and PDFs from $ X_i $, ho we can find the probability $$ P {X_1 <X_3 <X_2 < alpha-X_3 }. $$

Is
$$
P {X_1 <X_3 <X_2 < alpha-X_3 } =
int_ {x_3 = 0} ^ { infty}
int_ {x_2 =} ^ { alpha-x_3}
int_ {x_3 = 0} ^ {x_2}
int_ {x_1 = 0} ^ {x_3} f_ {X_1} (x_1) dx_1
f_ {X_3} (x_3) dx_3
f_ {X_2} (x_2) dx_2
f_ {X_3} (x_3) dx_3,
$$

or
$$
P {X_1 <X_3 <X_2 < alpha-X_3 } =
int_ {x_3 = 0} ^ { infty}
int_ {x_2 =} ^ { alpha-x_3}
int_ {x_1 = 0} ^ {x_3} f_ {X_1} (x_1) dx_1
f_ {X_2} (x_2) dx_2
f_ {X_3} (x_3) dx_3.
$$

Thank you.

Probability Distributions – Sample Estimatior Cube

We make subsequent throws of a false cube for which the probability of losing six is ​​1/6 – epsilon, the probability of falling from one is 1/6 + epsilon and the other eyes disappear with the same probability 1/6. Provide a consistent and unbalanced epsilon estimator parameter and calculate its variance. I need help to start my trip with this ad, it's so hard for me: /

Calculation of the probability of the p-persistent CSMA network

Suppose that, in a p-persistent CSMA network, a station, X, is ready to transmit data. All other stations are inactive for 5 time intervals once X is ready. What is the probability that X transmits its frame in the three slots after being ready?

What is the probability of identifying a user based on an interaction model?

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probability – The conditional joint distribution of exponential sums is the same as the distribution of the uniform order statistic

I have trouble proving the following proposition:

Let $ X_1, X_2, points, X_n $ to be i.i.d random variables distributed exponentially with parameter $ lambda $. Then the joint distribution of $ X_1, X_1 + X_2, X_1 + X_2 + X_3, points, X_1 + points + X_n $ given the condition $ X_1 + points + X_n = t $ is equal to the joint distribution of the order statistics $ (Y_1, dots, Y_ {n-1}) $ of the uniform distribution on $[0,t]$.

So $ f (x_1, points, x_1 + points + x_n | x_1 + points + x_n = t) = dfrac {f (x_1, points, x_1 + points + x_n)} {f (x_1 + points + x_n)} $. And I think that now I'm supposed to use the exponential property without memory of the exponential distribution but I do not see how.

Probability with percentages of population

The question is this: The American Diabetes Association estimates that 5.9% of Americans have diabetes. Suppose that a medical laboratory has developed a simple diagnostic test for diabetes accurate to 98% for people with the disease and 95% for those who are not. If the medical laboratory gives the test to a randomly selected person, what is the probability that the person with diabetes will receive a positive test?

I'm not sure where to start, but I thought the test positive 98% positive results for people with diabetes and the inaccuracy of 5% of the test indicating that you have a positive test while you do not do not do it. I note, however, that 94.1% of the population does not have diabetes, while 5.9% have diabetes, which means that the incorrect test of the positive for people without the disease is in greater demand.