A fair coin is tossed four times. Let X denote the number of heads occurring. Find the probability distribution, mean and variance of X.

Explanation

When a coin is toss 4 times we get the following possibilities:

`{HHHH, HHHT, HHTH, HTHH, THHH, THHT, TTHH,HHTT, THTH, ldots ldots, TTTT}`

A total of `16` possibilities

Let `x` be the random variable representing number of heads occurring in 4 tosses of a coin.

since probability of getting a head or probability of getting a tail are independent events and P(getting a head) = P(getting a tail)`=1/2`

`therefore` P(Head in first toss) and P(Head in second toss) and P(head in third toss) and P(tail in 4th toss) can be given by their individual products.

Note: `P(A cap B) = P(A)P(B)` where `A` and `B` are independent events.

Thus,

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