Question -
Answer -
Given X is any randomvariable whose binomial distribution is B (6, ½)
Thus, n = 6 and p = ½
q = 1 – p = 1 – ½ = ½
Thus, P(X = x) = nCx qn-x px,where x = 0, 1, 2 …n
It can be clearlyobserved that P(X = x) will be maximum if 6cx willbe maximum.
∴6cx = 6c6 =1
6c1 = 6c5 =6
6c2 = 6c4 =15
6c3 = 20
Hence we can clearlysee that 6c3 is maximum.
∴ for x = 3, P(X = x)is maximum.
Hence, proved that themost likely outcome is x = 3.