Question

Determine variance and standard deviation of the number of heads in three losses of a coin.

Answer 1

In any coin toss the P(H) = P(T) = 1212

A fair coin is tossed thrice. The sample space of three tosses of a coin is: {HHHTTTHHTTTHHTHTHTHTTTHH}{HHHHHTHTHHTTTTTTTHTHTTHH}

If X is the random variable, we can see that X = 0, 1, 2 or 3 depending on the # of heads.

P (X = 0) = P (no heads) = P (TTT) = 1818

P (X = 1) = P (HTT, TTH and THT) = 3838

P (X = 2) = P (HHT, HTH and THH) = 3838

P (X = 3) = P (HHH) = 1818

Therefore, given this probability distribution we can calculate the mean using the formula Mean of the probability distribution = ∑(Xi×P(Xi))∑(Xi×P(Xi))

⇒⇒ Mean =0×18=0×18 +1×38+1×38 +2×38+2×38 +3×18=128=32

Answer 2

coin 1 coin 2 coin3

h h h

h h t

h t h

h t t

t h h

t h t

t t h

t t t

7 heads