Math Is Fun Forum

dukebdx12

Member

Registered: 2007-03-21

Posts: 9

Power Series.

A fair coin is tossed repeatedly. The probability that the first head occurs on the nth toss is P(n)=(1/2)^n. When this action is repeated many times, the average # of tosses required until the first head is:
E(n)=sum from 1 to inf n*P(n)
This # is called the expected value of n

A) use the power series: 1/1-x = sum from 0 to inf of x^n, for |x|<1 to get a power series representation for f(x)=1/(1-x)^2 and give interval of convergence

B) what is the relation between E(n) and the series found in (a)?

C) what is the expected value of n? Be sure to give specific reason why you can make your conclusion.

I am completely clueless on this. If someone could just help me on each part not exactly answer it that would be very helpful. Thanks

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Power Series.

A) use the power series: 1/1-x = sum from 0 to inf of x^n, for |x|<1 to get a power series representation for f(x)=1/(1-x)^2 and give interval of convergence

In f(x)=1/(1-x)^2, 1/(1-x)^2 is your "x".  Plug it in to the right side of that equation.

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