Let X equal the number of flips of a fair coin that are required to observe the same face on consecutive flips.
a) find the p.m.f. of X.
p(x=2) = 1/2, p(x=3) =1/4, p(x=4) =1/8 ....
f(x) = (1/2)^x-1
b) give the values of the mean, variance, and standard deviation of X.
let u = (mean)
I know u = M'(0), and M(t) is given by:
M(t) = [summation from x =2 to infinity] e^(tx) * (1/2) ^x-1
I need to come up with a concrete expression for M(t) so I can differentiate, but can't remember anything that would help...what is the concrete expression for M(t)?
a) find the p.m.f. of X.
p(x=2) = 1/2, p(x=3) =1/4, p(x=4) =1/8 ....
f(x) = (1/2)^x-1
b) give the values of the mean, variance, and standard deviation of X.
let u = (mean)
I know u = M'(0), and M(t) is given by:
M(t) = [summation from x =2 to infinity] e^(tx) * (1/2) ^x-1
I need to come up with a concrete expression for M(t) so I can differentiate, but can't remember anything that would help...what is the concrete expression for M(t)?