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Let $\alpha$ and $\beta$ be two independent bernoulli random variables. What is the distribution of the product $\alpha(1-\beta)$ or $\alpha-\alpha\beta$. Thanks in advance. Actually, I want to know the distribution of $\delta=\alpha_1\beta_1+(1-\alpha_1)\alpha_2\beta_2+(1-\alpha_1)(1-\alpha_2)\alpha_3\beta_3$ where all $\alpha$ and $\beta$ are independent bernoulli random variables.

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closed as off-topic by RRL, mrtaurho, Cesareo, Jyrki Lahtonen, Lee David Chung Lin Apr 4 at 21:41

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Hint: $\alpha (1-\beta)$ also takes only the values $0$ and $1$; it is $1$ iff $\alpha=1$ and $\beta =0$.

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