An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
Let X denote the number of heads in the four tosses of the coin.
Then X is a random variable that can take the values 0, 1, 2, 3 or 4.
P(X=0)=Probability of getting no head (TTTT)
P(X=1)=Probability of getting one head (HTTT, THTT, TTHT, TTTH)
P(X=2)=Probability of getting two heads (HHTT, HTHT, HTTH, THHT, THTH, TTHH)
P(X=3)=Probability of getting three heads (HHHT, HHTH, HTHH, THHH)
P(X=4)=Probability of getting four heads (HHHH)
The probability distribution of X is
Mean, E(X) = ∑pixi=2
Therefore, the mean and variance of the number of heads obtained are 2 and 1, respectively.
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