Question

In a binomial distribution having 4 independent trials
it is known that the probability of no success is 16/81
Find: (a) the parameter p of the distribution,
(b) the mean and variance of distribution.​

Answer 1

Answer:

In a binomial distribution consisting of 5 independent trials, n = 5

The probability of 1 and 2 successes are 0.4096 and 0.2048 respectively.

5

C

1

p

1

(1−p)

5−1

=0.4096

5

C

2

p

2

(1−p)

5−2

=0.2048

5p(1−p)

4

=0.4096 _____ (1) 10p

2

(1−p)

3

=0.2048 ______ (2)

Divide equation (1) by (2), we get

2p

(1−p)

=2

5p=1

p=

5

1.