All Questions
Tagged with bounds-of-integration probability
9
questions
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27
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How to get a CDF value from a PDF when the required CDF is not within the defined area?
I have a density function f(x, y) = 1/2 for 0 ≤ x ≤ y ≤ 2 and 0 elsewhere. I am being asked to find the CDF value F(1, 3), but as you can see the three is past the range of the defined triangle, what ...
1
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44
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Integral bounds for $x\geq yz$
I am having trouble understanding the integral bounds.
From what side should my understanding go (first or second?):
first: as $z$ is between zero and one, $y$ is also between zero and one, thus $x$ ...
- 2,527
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2
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419
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Double integral setup - Uniform distribution
I am currently trying to understand a specific component of a probability problem involving setting up the proper bounds on a double integral.
In the problem, $X_1$ and $X_2$ are independent Uniform $(...
-1
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1
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186
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How do you find the bounds for a joint probability distribution function?
$$\begin{aligned} f(x, y) &=\begin{cases}1/(x^{2} y^{2}) & \text { für } &x \geq 1, y \geq 1 \\[1ex] 0 &&\text { sonst. }\end{cases}\\[2ex] V&:=X Y\end{aligned}$$
Find the ...
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63
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Estimate of the ratio $\frac{1}{\sqrt{2\pi}}e^{-x^2/2}(1-\text{erf}(x))$ (for standard normal distribution)
Define the probability density and cumulative probability of the standard Gaussian:
$$
f(t) =\frac{1}{\sqrt{2\pi}} e^{-t^2/2}, \text{erf}(x) = \int_{-\infty}^x f(t) dt.
$$
How can I prove that the ...
- 7,534
1
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1
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386
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What does this integral notation mean?
I'm talking about the integral part that is highlighted:
Should I interpret the top one highlighted as the upper bound of integration and the bottom one as the lower bound? That's the only ...
- 195
2
votes
2
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109
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Is there a bound such that $\mathbb E(X^n)-\mathbb E(X)^n \le c; \quad n \in \mathbb Z_+.$
Any help on proving a bound such that:
$\mathbb E(X^n)-\mathbb E(X)^n \le c; \quad n \in \mathbb Z_+.$
$X$ is the R.V. in the range of $[0,1]$
I am looking for something like Popoviciu's inequality ...
- 145
3
votes
1
answer
167
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Distances between $3$ random points on $[0,1]$
Suppose $3$ points are drawn uniformly at random from $[0,1]$. Call them $x_1,x_2,x_3$ with $x_1\leq x_2\leq x_3$. I am interested in the distances between them.
Fix $0<a<b<1$. I want to ...
- 3,880
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Integrating the bivariate normal distribution [duplicate]
Let $X$ and $Y$ have the bivariate normal density function,
$$ f(x, y) = \frac{1}{2 \pi \sqrt{1 - p^2}} \exp \left\{ - \frac{1}{2(1 - p^2)} (x^2 - 2pxy + y^2) \right\} $$
for fixed $p \in (-1, 1)$. ...
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