1.

The mean and variance of a bianomial distribution are 4and3 respectively. Fix the distribution and find (x >_1)

Answer»

ong>ANSWER:

For a biomial distribution, E (X) = np and Var (X)= npq ( where p is the probility of success and q is the probility of FAILURE where q=1-p ).

NOTE The Following

np= 3

npq= ⅔

Thus, we have that 3q = ⅔ and this q= ½.

SINCE We know that q=1-p, then p=½. plugging the value

of p into np=3, we get that n=6. Now that we know the

value for n,p and q, we can plug these into the binomial

mass function so that we can find the binomial mass

function is p( X=x)=(n^x) p^x. q^n-x

and so with n=6 ,p=½,q=½ and X=5.

.We have the following.

P (X=5)=(⅚)(0.5)⁵(0.5)¹

3

= ___

32

Therefore, the probability of time success is

0.09375.


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