All Questions
Tagged with density-function conditional-probability
22 questions with no upvoted or accepted answers
7
votes
0
answers
702
views
Spinograms vs. conditional densityplots
I have a binary response variable (hail) and multiple continuous predictor variables. My aim is to understand the linear/non-linear relationship of the predictors to the response to be able to justify ...
- 511
3
votes
0
answers
118
views
Conditional Distribution of Multivariate Gaussian given Linear Inequalities
Consider a multivariate Gaussian $Y\sim\mathcal{N}(\mu,\Sigma)$ of dimension $n$. For fixed $c\in\mathbb{R}^n, A\in\mathbb{R}^{m\times n}$ and $c\in\mathbb{R^m}$, what is the conditional distribution ...
- 31
2
votes
1
answer
234
views
Questions about the conditional Radon-Nikodym derivative
Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space and $X:(\Omega, \mathcal{A})\rightarrow (\mathcal{X}, \mathcal{F})$ and $Y:(\Omega, \mathcal{A})\rightarrow (\mathcal{Y}, \mathcal{G})$ ...
- 863
2
votes
0
answers
806
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min/max and probability distributions
We have two identically distributed, independent, uniform variables on interval $[0,1]$ : $X_{1}$, $X_{2}$. And $Y_{1}=\max(X_{1},X_{2})$, $Y_{2}=\min(X_{1},X_{2})$. I want to find distribution $f(y_{...
- 273
1
vote
1
answer
159
views
Calculating PDF conditioned on event
I'm confused about problems where we calculate a PDF conditioned on an event.
Consider this simple problem:
We have two random variables, X and Y, X is uniformly distributed on [a,b], and Y is uniform ...
1
vote
1
answer
26
views
Would this way of evaluating this probability be correct?
Suppose I have a discrete variable $S_t$ and a continuous variable $X_t$. Further, suppose I wish to evaluate $P(S_t=s_t)$. Would the below derivations be correct?
\begin{align}
P(S_t=s_t)&=\int P(...
- 1,226
1
vote
0
answers
132
views
Conditional Density Function on Underlying Exponential
Problem Statement: Suppose $Y_1, Y_2,\dots, Y_n$ are a random sample from an exponential distribution with mean $\theta.$ Let $\displaystyle U=\sum_{i=1}^n Y_i.$ Find the conditional density function ...
- 6,039
1
vote
0
answers
54
views
joint and conditional density function
Let $f(x,y,z)$ be the joint density function. I found a reference that this joint density can be written as
$f(x,y,z) = f_1(x|y,z)f_2(y|z)f_3(z)$
I'm wondering if there are alternative forms to ...
- 387
1
vote
0
answers
80
views
Conditional Probability involving condition on two RVs
Suppose X,Y~exp(2) and are independent. Let W=X+Y.
How do I set up integrals to calculate the following:
f(W|X>Y)
E(W|X>Y)
Thanks!
- 21
1
vote
0
answers
14
views
bivariate conditional joint sensor model
I am struggling to find $P\left( V_t | z \right)$ from $P\left( V_t | z , V_p \right)$. Here $z$ and $V_p$ are independent variables.
...
- 11
1
vote
0
answers
536
views
Changing a conditional probability to a deterministic function
Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...
- 286
1
vote
0
answers
392
views
How to integrate out a continuous r.v. from a mixed joint density
Say I have a continuous variable $C \sim N(0, 1)$, which was observed in a few points:
obsC <- seq(-1.5, 1.5, by = 1)
I also have a discrete variable $D \in \{...
- 2,617
1
vote
0
answers
17
views
conditional PDF bivariated Birnbaum Saunders
According to theorem 3.1 of this article here, If $(T_{1},T_{2})\sim BVBS(\alpha_{1},\beta_{1},\alpha_{2},\beta_{2},\rho),$ then:
The conditional PDF of $T_{1},$ given $T_{2}=t_{2},$ is given by:
$$...
- 148
0
votes
0
answers
22
views
Determining Distribution for Conditional Probability
I have that the conditional probability density of $Y|X$ is as such
$f_{Y | X} \propto x^{y - 1}(1-x)^{n-y-1}\alpha^{n-y}\beta^{y}$
where $\alpha, \beta$ are constants in $(0, 1)$, $x$ is a random ...
- 13
0
votes
1
answer
35
views
Conditioning once or twice?
Let's say we have two random variables $Z \in \mathcal{Z}$ and $X \in \mathcal{X}$ with joint density $p_{Z,X}(z,x)$ with respect to a base measure. The density is assumed to factor as
$$ p_{Z,X}(z,x) ...
- 311
0
votes
0
answers
48
views
Converting an integral into a probability of some event
Suppose that $X_1, X_2, .....X_n$ are iid random variables from some continuous distribution $F$. Show that $$\int_0^{\infty}(1-F(s+t))f(s)ds=\mathbb{P}(X_1>X_2+t, X_2>0)$$
$$$$Consider the ...
- 217
0
votes
0
answers
51
views
Derive E[Y|X] when the joint probability is given
Now, consider joint density of $X, Y$ :
$$
f_{X, Y}(x, y)=\left\{\begin{array}{l}
\frac{1}{\pi} ; X^2+Y^2<1 \\
0 ; \text { Otherwise }
\end{array}\right.
$$
Derive $E(Y \mid X)$.
I know how to ...
- 25
0
votes
0
answers
120
views
Conditional Density Of Independent Bernoulli Random Variables Given Their Sum
Let Yi's be m independent Bernoulli random variables with corresponding success probabilities pi's, and let S = sum of Yi's.
I am trying to figure out a way to find the given conditional probability, ...
- 1
0
votes
0
answers
198
views
decomposition of joint density of multiple variables
I'm considering an EM algorithm of correlated random effects model
$y_{it} = \beta x_{it} + \mu_i + \varepsilon_{it},(i=1,...,n;t=1,...,T)$
where $y_{it}$ and $x_{it}$ are observed, but $\mu_i$ and $\...
- 387
0
votes
0
answers
56
views
Conditional density under conditional indepencence?
Let $X,Y,Z$ three random variables such that the joint density can be factorized as
$$f(x,y,z) = f(x \mid z) f(y\mid z) f(z).$$
This is, I am assuming conditional independence of $X$ and $Y$ given $Z$....
- 1
0
votes
1
answer
179
views
Compute $E(X_1|X_1+X_2)$ $X_1, X_2$ both iid $Exponential(1)$
I recently stumbled across this question on CV:
Conditional expectation conditional on exponential random variable
And really liked the answer provided by @Rush, but I wanted to try to compute this ...
- 297
0
votes
0
answers
36
views
Is the following integral of a pdf an identity, i.e. always true?
I am reading a paper and the author starts a proof with this
$$
p(\hat{R}|R) = \int p(\hat{R},\theta|R)d\theta
$$
p is the density function.
Is this something that is always true? Can you help me ...
- 1,275