I'm stuck on one of the question in our online test in statistics:
Suppose that X ε [1,2,..., ] is discrete random variable that follows a geometric distribution with mean 3.74.
What is the probability that X is an even number?
Give your solution accurate to 4 decimal places.
my idea was:
from geometric sequence:
3.14=1/theta -> theta=0.26737968
and then use P(X=x)=(1-theta)^x-1 * theta
to get P=0.1373945
however don't know if that's what the question is asking about (i.e what is the 'successs' in this geometric distribution, number being even?) another idea was to put:
P(X=2x), if that makes any sense, to account for the number being even however don't know how to go from there
would appreciate any help
Thank you so much!
Maybe I don't understand subject so well, but we only did infinite series sums if
-1<r<1 so don't know how to compute the sum with r=2.
I guessed to use formula
and sum it from i=1 up to infinity
but I don't know how to obtain a numerical answer not in terms of ratio of i.