NDA Math Binomial Theorem

Concept:
For the binomial distribution of probability
- Mean =np
- Variance =npq
Where n is the total number of cases,
p is probability of favorable cases and q is probability of unfavorable cases(1 - p)
Calculation:
Given mean=np=‌

2

3

and variance =npq=‌

5

9

‌

‌ variance ‌

‌ mean ‌

=‌

‌ 5 9

2 3

q=‌

5

6

p=1−q=‌

1

6

np=‌

2

3

n=4
∴ The probability that random variable D=2
P=‌nC2p2qn−2
P=‌4C2×(‌

1

6

)2×(‌

5

6

)2
P=6×‌

1

36

×‌

25

36

P=‌

25

216