I have a set of probability corresponding to Bernoulli experiment. How to draw Bernoulli random number given these specific probability from a uniform(0,1) distribution. I know we can draw from binom, but using uniform distribution can vectorize the operation and make it so much faster.
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It sounds like you're asking how to simulate independent draws from a Bernoulli distribution with a given probability $p$ when all you have is independent draws from a uniform distribution on $[0, 1]$. That's easy: for each value $x$ drawn from the uniform distribution, return 1 if $x < p$ and 0 otherwise.
answered Oct 15, 2016 at 1:03
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$\begingroup$ Why is that Bernoulli number? Can you explain it a bit more? $\endgroup$– MLEOct 15, 2016 at 1:06
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1$\begingroup$ Why is the result Bernoulli-distributed, you mean? Because all that's required is to return 1 with probability $p$, and the uniform distribution on $[0, 1]$ means that the chance of $x$ landing in $[0, p]$ is $p$. $\endgroup$ Oct 15, 2016 at 1:09
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$\begingroup$ Yes, why the result is Bernoulli distributed why when x<p, return 1. Still very confused. Why "the uniform distribution on [0,1][0,1] means that the chance of xx landing in [0,p][0,p] is p" $\endgroup$– MLEOct 15, 2016 at 1:53
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$\begingroup$ Because that's how the uniform distribution is defined. I'm not sure what more there is to say without getting into measure theory or something, which I doubt you would find enlightening. $\endgroup$ Oct 15, 2016 at 3:05