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adnanchowdhury

  • 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. xEnOnn
    • 4 years ago
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    Is the answer 0.72?

  2. xEnOnn
    • 4 years ago
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    ?

  3. adnanchowdhury
    • 4 years ago
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    no, then answer is: 0.064 (= 8/125)

  4. Zarkon
    • 4 years ago
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    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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