Distribution of Product of a Bernoulli Random Variable and (1- Another Bernoulli Random Variable) [closed]

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.

closed as off-topic by RRL, mrtaurho, Cesareo, Jyrki Lahtonen, Lee David Chung LinApr 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 $$\beta =0$$.