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Conditional probability for 3 random variables failing

Now, if I marginalize $x_0$ on the l.h.s., I get: $$ q(x_{t-1}|x_t) = \int dx_0 q(x_{t-1}|x_t,x_0) q(x_0) $$ No. Applying the Law of Total Probability under the condition of $x_t$ gives: $$q(x_{t-1}\...
Graham Kemp's user avatar
2 votes

what is probability density and distribution of X?

Will density become zero if we differentiate distribution w.r.t y? Yes, $\dfrac{\partial \mathsf P(X\leq x)}{\partial y} = 0$ because $\mathsf P(X\leq x)$ is not a function of $y$ . But... Why would ...
Graham Kemp's user avatar
1 vote

Lumbroso "dice roller", correctness of the algorithm for 32 bit integers

(A) "Am I Correct ?" : Yes , there is a Corner-Case Bug in the C Code. Consider 32Bit numbers like this : $v=00000000000000000000000000000001$ $c=00000000000000000000000000000000$ $n=...
Prem's user avatar
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1 vote

Lumbroso "dice roller", correctness of the algorithm for 32 bit integers

I agree the C algorithm is (probably) flawed. The author states the correctness of the program depends on the loop invariant "$c$ is uniformly distributed over $\{0, \dots, v-1\}$." Let us ...
msantama's user avatar
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Aggregates and Psuedorandomness

If $0<N<2^{32}$ then there exist subsets of size $N$ with different averages, for example the subset of the least $N$ numbers has a strictly smaller average than the subset of the largest $N$ ...
Lieven's user avatar
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Periods of certain lagged Fibonacci sequences

Defining the RNG First off, as the comments in random.cs state, Microsoft's implementation is based on an algorithm from Numerical Recipes (specifically the 2nd edition: newer editions recommend a ...
trillian's user avatar
  • 101

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