New answers tagged conditional-probability
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Why do Denoising Diffusion Probabilistic Models (DDPM) add noise according to $\sigma_t$ during sampling?
I also searched long for an answer to this question but managed to convince myself that this is similar to the StyleGAN model. In StyleGAN, we also sample from a Gaussian distribution (just as we do ...
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4
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Accepted
Conditional probability of having intellectual disability
The problem here is the notation in the paper (not your formula). ID/DD in this context means ID or DD (not ID and DD). In your formula, $P(ID,DD) = P(ID \cap DD)$, but in the paper ID/DD means $P(...
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Conditional expectation of a continuous random variable given a discrete random variable
The question of how to compute $E[T|K = k]$ has been addressed by Xi'an in the comment. More explicitly, assume $p_k := P(K = k) > 0$ for each $k$, then the conditional density of $T$ given $T = k$...
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Conditional expectation of random variables
$E[X] = 6$ because in a very long series of rolls arbitrarily close to $1/6$ of all outcomes will be $1,$ whence the mean waiting time to observe a $1$ will be arbitrarily close to $1/(1/6)=6.$
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Conditional expectation of random variables
Your argument is correct (+1). The step of deriving the conditional distribution of $Y$ given $X = x$ may be made a little more formal as follows: for $x \geq 2$ and $0 \leq y < x$,
\begin{align}
...
- 13.4k
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Complementary events and conditioning
To see why $P(A\mid B) + P(A \mid B^C) = 1$ is not generally true, consider the case where $A$ is always guaranteed to happen, regardless of what happens with $B$. Then both $P(A \mid B)$ and $P(A \...
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Complementary events and conditioning
The conditional probability that you don't have red hair, given that you are male, is more than $0.9.$
The conditional probability that you don't have red hair, give that you are not male, is more ...
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Complementary events and conditioning
All you need is just one counterexample.
Consider $\Omega = \{1, 2, 3\}$ with $P(\{1\}) = P(\{2\}) = P(\{3\}) = \frac{1}{3}$, $A = \{1, 2\}, B = \{2, 3\}$, then
\begin{align}
& P(A|B) = \frac{P(\{...
- 13.4k
4
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Accepted
How does one calculate $\text{Var}(E[Y|X])$? and other related quantities
When you specify the conditional expectation (or other moment) of a random variable $Y$ given a specific value of the conditioning variable $X=x$, the result is a function of the argument $x$. In ...
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3
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Accepted
Sampling from an approximate distribution to estimate posterior mean
The issue with the question is that the expression$$\mathbb E[\theta_1|x]$$is not well-defined:
either $(\theta_1,\theta_2)$ is considered a random vector with joint prior $\pi(\theta_1,\theta_2)$, ...
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