Question Details

For a Binomial distribution B (n, p),E(x)/V(x)is is equal to: (symbols have their usual meaning)

Options

A

1/p2

B

1-p

C

1/1+P

D

1/1-P

Show Answer

Correct Answer :

Option D

1/1-P

Solution :

The correct option is 1/1-P.

Let us understand the step-by-step derivation for the ratio of the expectation to the variance of a Binomial distribution, denoted as B(n, p).
For a Binomial distribution with parameters n (number of trials) and p (probability of success):
1. The expected value or mean, denoted as E(x), is given by:

E(x)=np

2. The variance, denoted as V(x), is given by:

V(x)=npq

where q is the probability of failure, defined as:

q=1-p

Substituting this, we get:

V(x)=np(1-p)

Now, we find the ratio of E(x) to V(x):

E(x)V(x)=npnp(1-p)

By cancelling out the common term np in the numerator and the denominator, we obtain:

E(x)V(x)=11-p

Using P (uppercase) as specified in the option, this is equal to:

11-P

Hence, the ratio is indeed 1/1-P.

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