Is the object $u$ which takes a value of 1 with probability $1/2$ and a value of $0$ with probability $1/2$ a random variable?

If not, what is the proper mathematical term for an object like this? Furthermore, what would be the random variable (+ probability distribution?) equivalent?

  • $\begingroup$ Not it isn't; was just curious about some terms I stumbled upon. $\endgroup$ – bonifaz Sep 22 '15 at 11:20

What you are describing is a Bernoulli distribution with parameter $p = 0.5$

$$ f(x) = \begin{cases} p & \text{if }x=1, \\[6pt] 1-p & \text {if }x=0.\end{cases} $$

So in this case $u$ is a random variable with sample space $u: \Omega \rightarrow \{0, 1\}$, that follows a Bernoulli distribution.

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  • $\begingroup$ Is there any connection between this distribution and a random variable? $\endgroup$ – bonifaz Sep 22 '15 at 10:41
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    $\begingroup$ In your case $u$ is a random variable that follows Bernoulli distribution. If those terms are not clear refer to some statistics handbook for more details. $\endgroup$ – Tim Sep 22 '15 at 10:43

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