If x ~ B(n,p) , what would be the least value of the variance with n=16?
How do we calculate least value.
Thanks in advance.
3 Replies
intermediate(ipc)course
(no)
(1460 Points)
Replied 31 May 2012
x ~ B(n,p)
x ~b(16,P)
p = 1/2
q = 1/2
sd = root npq
= root 16*1/2*1/2
=root 4
=2
(sd)^2 = variance
(2)^2 = variance = 4
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 01 June 2012
variance is np(1-p) os we have to find the least value of p*(1-p) p(1-p) = p - p^2. for this function the maximum value is 0.25 which it will attain at p = 0.5. and minimum value is attained at p =0 or p=1 which is 0,. (the function is an inverted parabola so it will have a maximum but the boundaries of the interval are the minimum values) which is 0 so least value is 0 maximum value is 4
priya
(Student)
(64 Points)
Replied 02 June 2012
Thanks for the answers. 4 will be the maximum variance (n/4). For minimum variance i got 0, but the answer given was 2. Hence got the doubt...
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