Question

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.

Answer 1

Is the answer 0.72?

Answer 2

?

Answer 3

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

Answer 4

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

\[\sum_{v=1}^{2}P(X_1=v,X_2=3-v)\]