This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...
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1answer
14 views
Calculate failure of component by central limit theorm
A component in a device fails one time per 24 hours (on average). How many spare parts should be in order to verify that the probability they will be enough for one week is 95%? Use central limit ...
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2answers
15 views
When do we use a two-tail hypothesis testing instead of a one tail?
I always use a two-tail hypothesis testing unless I am told to use a one tail. Is that a good way of going about solving problems or is there a flaw to that way of doing things?
Also, if they say use ...
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0answers
8 views
distribution of maximum of $n$ Pearson correlations
$\mathbf{x}=[x_1,x_2,...,x_m]^{\top}$ is a vector of length $m$ and $\mathbf{y_1}, \mathbf{y_2}, ..., \mathbf{y_n}$ are similarly $n$ vectors of length $m$.
If the elements of $\mathbf{x}$ and ...
1
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1answer
17 views
Equivalence of uniform distribution
Behind a square grid evenly (i.e. uniform distribution) scattered dots.
Could it be considered identical to a sequence of independent events with probability $\frac{1}{N}$ to hit the cell with dot? ...
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0answers
15 views
Difference between population with duplicates and no duplicates when estimating the size of a sample
We have a population where the mean is 50.5 and the variance is 833.25, we need to calculate the sample size given a 95% confidence and the sample mean lying 3 units of the population mean.
So if I ...
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0answers
20 views
Total variation distance for probability measures
I'm having troubles solving this problem, any help will be appreciate :)
Let $(\Omega,\mathcal{F})$ a measurable space, and let $\mu, \ \nu$ probability measures on $\mathcal{F}$. It's well know that ...
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1answer
15 views
Function of a Poisson Point Process
Let $(P_s)$ be a Poisson point process on a state space $X$ with intensity measure $\mu$. Let $f(s,x)$ be a non-negative integer valued function on $[0,1]\times X$. Let $N = \sum_{s\leq 1} \mathbb ...
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1answer
16 views
Estimate the number of elements by random sampling with replacement
Setup:
$N$ numbered balls are in a bag. $N$ is unknown.
Pick a ball uniformly at random, record its number, replace it, shuffle.
After $M$ samples, of which we noticed $R$ repeated numbers, how can ...
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0answers
14 views
Why would I use Bayes' Theorem if I can directly compute the posterior probability?
I fully understand the mechanics of Bayes' Theorem. However, I am wondering when do I need to use it? If I am able to compute the posterior probability directly from measured data, why would I need to ...
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0answers
36 views
Can we use ln to integrate an expression?
i need to calculate the moment generating function for the geometric distribution, and i was wondering if we can use ln to integrate a complex expression just like we can use ln to differentiate a ...
3
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2answers
24 views
Dice probability over multiple rolls.
What is the probability of rolling one or more 6's using 3 six sided dice (1...6) that are rolled three times?
How does multiple rolls influence the probability, is it simply 3 times the probability ...
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0answers
32 views
A stochastic programming with a chance constraint
Let $X$ be a bounded positive variable with an unknown probability density function (PDF) and $f(X)$ be a differentiable positive function.
$$\begin{align*}
&\min/\max ...
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3answers
46 views
Calculating $E[(X-E[X])^3]$ by mgf
Calculate by mgf $E[(X-E[X])^3]$ where
a. $X\sim B(n,p)$
b.$X\sim N(\mu,\sigma)$
Before I begin I thought symbolizing $Y=X-E[X]$ and then I'd derivative $M_Y(t)$ three times substitute ...
1
vote
3answers
46 views
$3$ dice are thrown simultaneously
I have a doubt in this question:
Three dice are thrown simultaneously. Find the probability that:
All show distinct faces
Two of them show the same face
My approach is for 1):
$$
...
0
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1answer
20 views
Conditional distribution of a function of random variables
I have a question about conditional distribution. Suppose we have three independent random variables $X_1$, $X_2$, $X_3$.
Then we have mapping $Y_1=g(X_1, X_2)$. The mapping is not necessarily an ...