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We are given a random variable $X$ with PDF: \begin{align*} f(x ; p) &= p^x(1-p)^{1-x} \ , \\ \end{align*} where $0 \leq p \leq 1$ is the parameter and the support is $x \in \{0,1\}$.

Anyone knows what the name of this distribution is? And if so, could you please help me understand how I can infer to that? I only know of simple distributions such as uniform, gaussian...etc.



Update!

Thanks Minus One-Twelfth! I appreciate the quick answer, but I was hoping for some more elaboration on how I can infer to the distribution type.

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  • $\begingroup$ Note that $f(0;\,p)=1-p,\,f(1;\,p)=p$. $\endgroup$ – J.G. Mar 23 at 11:27
  • $\begingroup$ "how I can infer to the distribution type" You either know the name or you don't. Regardless, knowing the name won't help you use it. The actual distribution (which you have a nice formula for there) is what lets you do that. $\endgroup$ – Arthur Mar 23 at 11:34
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This is the Bernoulli distribution. Not sure what you mean by "infer to that".

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This is the binomial distribution with $n=1$ trials $\big(f(x)=\binom{1}{x}p^{x}(1-p)^{1-x}\big)$, otherwise known as the Bernoulli distribution. It seems you are looking for intuition, so just note that, given $p$, the codomain of $f(x)=p^{x}(1-p)^{1-x}$ with $x\in\{0,1\}$ has cardinality 2; namely, $f(x)\in\{p,1-p\}$, which makes sense because if $x=0$, we get the probability of "failure" $1-p$, and if $x=1$, we get the probability of "success" $p$.

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