How unfair!
Consider an unfair coin that is biased so that it falls heads of the time. If you flip it five times, the expected value of the number of tails is 3.
What is the variance of the number of tails in five flips?
The answer is 1.200.
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1 solution
Moderator note:
Note that "V(0)" isn't a standard term. I am guessing that you are calculating .
A better approach is to either work directly from first principles, or to use the formula for variance of a binomial distribution.
P(0 tails) = 32/3125, so V(0) = 288/3125
P(1 tail) = 240/3125, so V(1) = 960/3125
P(2) = 720/3125, so V(2) = 720/3125
P(3) = 1080/3125: V(3) = 0
P(4) = 810/3125: V(4) = 810/3125
P(5) = 243/3125: V(5) = 972/3125
V(total) = (288 + 960 + 720 + 810 + 972)/3125 = 3750/3125 = 6/5 = 1.2