Expected Sequences in a Random Events

[AliDimayev]

How many heads in a row would you expect to find if you toss a fair coin 8 times?







I am thinking that the probability of 3 heads is 1/8 and since you have 8 tosses, that would give an E(x) of 1. So I am guessing that 3 is the number of heads one would expect to see in a fair coin is tossed 8 times. But I am not sure... Any help?

 

[rock.freak667]

You can do this in two ways, the basic method and the shorter method.

The basic way is to use the definition of E(X)= ∑_{all x} x*P(X=x)

Write out in a tabular form, the distribution

x
P(X=x)

x is the number heads obtained, so x goes from 0 to 8.


The other way is to see if the question can be fitted to a special type distribution.

 

[statdad]

I need some clarification: which question is of interest:

1) How many heads would you expect to occur during 8 flips of a fair coin?

2) If a fair coin is flipped 8 times, how long a sequence of consecutive heads would you expect to occur? (I phrased this from your wording "How many heads in a row...")

These questions are not the same.