Question

suppose x is binomially distributed with parameter n and p if E(x)=5 AND VAR(x)=4 find n&p

Answer 1

Concept:

Mean = np

Variance = npq  

Here,

n is number of trials

p  is probability of success

q is probability of failure

See the attachment for detailed solution

I hope this answer helps you

Answer 2

Given:

E ( x ) = 5

Var ( x ) = 4

To find:

The values of n and p

Solution:

E ( x ) is the mean.

Hence,

By formula,

Mean = n * p

n * p = 5

Variance = n * p * q  

n * p * q = 4

Substituting,

5 * q = 4

q = 4 / 5

We know that,

p + q = 1

p + 4 / 5 = 1

p = 1 - 4 / 5

Hence,

p = 1 / 5

1 / 5 * q = 5

q = 5 * 5

Hence,

q = 25