# Show that the variance of a binomial distribution

• January 2nd 2010, 06:20 AM
Show that the variance of a binomial distribution
Show that the variance of a binomial distribution with parameters n and p cannot exceed n/4.
• January 2nd 2010, 06:54 AM
Moo
1. What is the variance of a binomial distribution (n,p) ?

2. What is the maximum value of the function $f(x)=x(1-x)$, when $0\leq x\leq 1$ ?
• January 3rd 2010, 03:07 AM
Quote:

Originally Posted by Moo
1. What is the variance of a binomial distribution (n,p) ?

2. What is the maximum value of the function $f(x)=x(1-x)$, when $0\leq x\leq 1$ ?

$\sigma^2 = n \theta(1- \theta)$

and max value of $f(x) = x(1-x) = 0$ when we substitute the value of x= 1
• January 3rd 2010, 03:59 AM
mr fantastic
Quote:

$\sigma^2 = n \theta(1- \theta)$
and max value of $f(x) = x(1-x) = 0$ when we substitute the value of x= 1
Maximum value! NOT minimum value. Draw the graph of $y = x(1 - x)$ over the domain $0 \leq x \leq 1$. (Did you bother to do that before just plucking a random [wrong] answer out of the air?). The maximum value occurs at the turning point. Drawing parabolas and finding turning points is something you should have learned how to do long ago. Do you realise that work previously studied is assumed to be understood?