Question

Four fair coins are tossed once. Find the probability mass function, mean and variance for number of heads occurred.

Answer 1

Let ‘X’ be the number of heads occurred when four coins are tossed once. Hence ‘X’ can take the values 0, 1, 2, 3 and 4. 

When 4 coins are tossed, the sample space is, 

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Probability mass function 

Mean 

= 5 - 4 = 1