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## anonymous 4 years ago The random variable X has the distribution Geo(0.2). Two independent values of X are found. Find the probability that the total of these two values is 3.

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1. anonymous

Is the answer 0.72?

2. anonymous

?

3. anonymous

no, then answer is: 0.064 (= 8/125)

4. Zarkon

so the pmf is $P(X=k)=(1-.2)^{k-1}.2$ if $$X_1$$ and $$X_2$$ are independent realizations of $$X$$ then the joint pmf is given by $P(X_1=m,X_2=n)=(1-.2)^{m-1}.2(1-.2)^{n-1}.2$ then the probability you are looking for is given by $\sum_{v=1}^{2}P(X_1=v,X_2=3-v)$

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