All Questions
Tagged with sum probability
27
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PDF of difference of uniform distributions [duplicate]
Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation.
Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
1
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1
answer
164
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Show that for random variable $X$ with $N = \{1, 2, \ldots \}$, $E(X) = \sum_{n = 1}^\infty P(X \geq n)$ [duplicate]
Prove that for random variable with natural numbers from 1 to infinity the expected value $E(X)$ is equal to $\sum_{n = 1}^\infty P(X \geq n)$. Is this the mathematically correct way to prove it? And ...
- 45
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154
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The third central moment of a sum of two independent random variables
Is it true that in probability theory the third central moment of a sum of two independent random variables is equal to the sum of the third central moments of the two separate variables?
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Non-negative fat-tailed "almost stable" family of distribution with finite mean?
I am looking for a finite-dimensional family of distributions $F_X(x)$ with all the following properties:
Supported on $[0, +\infty)$,
Fat tailed, i.e. $(1-F_X(x)) \sim x^{-\alpha}$ for $x\to +\infty$...
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2
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1
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93
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Estimating the probability of a sum of events
I have n machines that use the same utility. Each machine randomly demands a unique f_n flow rate of the utility once every h_n hours on average. Each machine's demand event lasts for about m_n ...
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2
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1
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58
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Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?
If $X_1,X_2$ are dependent but identically distributed, it seems obvious that $P(X_1+X_2\geq2C) \leq P(X_1\geq C)=P(X_2\geq C)$. At least if we additionally assume that the joint distribution is ...
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1
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77
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Probability of joint dependent events
I'm having trouble finding a way to do this calculation and checking if I'm correct:
Let $X_1 \sim Exp(2)$ and $X_2 \sim Exp(2)$ be independent random variables $\left(f_X(x) = 2e^{-2x}\right)$, ...
- 113
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3
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795
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If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed]
If $20 $ random numbers are selected independently from the interval
$(0,1) $ what is the probability that the sum of these numbers is
at least $8$?
I tried to take this question https://math....
- 377
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168
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Concentration of sum of geometric random variables taken to a power
I am interested in techniques for showing the concentration of sum of $n$ iid geometric random variables $X_1, X_2, \cdots, X_n$ (number of trials until success), say with success probability $p = 1/2$...
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157
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X~Unif(0, 1) ; X1 + X2 + ... X6 = 1 ; Y = sum(X1...X6) ; VAR(Y) =?
Let $X_i$ ~ Unif(0, 1) s.t.
$X_1 + X_2 + ... + X_6 = 1$
Let $Y = X_1 + … X_6$
What is $Var(Y)$?
(Also the case when it's $X_n$)
Purpose for the curious:
I'm trying to rank confidence for softmax ...
- 93
2
votes
1
answer
40
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Making a discrete probability question continuous
I'm trying to figure out how many coin flips you'd need to have a greater than 50% chance of having seen a heads, given a biased coin with heads probability $p$.
From this question we can see that ...
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1
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69
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probability distribution of a sum of random variables [closed]
Suppose we have a random variable $X$
$P[X=-1]=1/3$, $P[X=0]=1/3$ and $P[X=1]=1/3$
now let $Y=X^2$
we have $n$ independent realizations of $Y$ $(Y_1, Y_2,......, Y_n)$ what is the probability ...
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11
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4
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1k
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How to interpret sum of two random variables that cross domains?
suppose we have two discrete random variables:
$X: \{$6 sided dice rolls$\}$ $\rightarrow \{1..6\}$ (following uniform distribution)
$Y: \{$coin flips$\}$ $\rightarrow \{0,1\}$ (following uniform ...
- 231
2
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1
answer
65
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Force sum of random varables to equal to 1 [duplicate]
Suppose I have 3 random variables, $X1, X2,X3$. Define $Z$ as:
$Z=X1+X2+X3$
I want to force $Z$ to equal 1 for every "realization" of $X1,X2,X3$ ($X_i \sim Beta(a_i,b_i))$. As an example, let $X_i$ ...
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117
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Summation of two Gaussian distributed data with different coefficient of mean and variance
I need some help on Gaussian distribution. i have two dataset, both are identical and independent distributed, but having mean as 2μ_1 and μ_2, same scenario for the variance. How can I add them?
...
