Expected Value of X in Binomial Trials

[nbalderaz]

In a series of three binomial trials with p=.4, a random variable, X, is assigned to the outcomes to form a base 2 number, with 1 associated with success(S), and 0 associated with failure(F). For example, SFS->101=5.

A) Find the expected value of X, E[X].
(Answer 2.80)

B) Find the expected value of X if P=.5
(Answer 3.5)

 

[TenaliRaman]

What have u done so far?

-- AI

 

[Lele]

I think you mean 3 bernoulli trials and not binomial trials. Remember bernoulli trials have just 2 outcomes (1 and 0 in your question).
Since you know the 3 digit number (from the SFS or other combinations) just use definition of Expectation.
E[X] = Summation (x*P(x))
In your case the x would be 1*2^n and 0*2^n(which is 0 so can ignore)...n is the power corresponding to the placing of the number.
As for a number at the unit's place, you would have 1*2^0.
For Bernoulli the expectation is just p and then use the definition to obtain the result.

Hope this helps.