# Math Help - [SOLVED] Need help with integration

1. ## [SOLVED] Need help with integration

Hi,

I am trying to integrate the following

Integral of x*n!/x!(n-x)! *p^(x)*(1-p)^(n-x)dx limits being (x=0,n)

I applied the rule of integration by parts as follows -

Let u = x & dv = n!/x!(n-x)!*p^(x)*(1-p)^(n-x)dx

Therefore, du=dx
V= integral n!/x!(n-x!)*p^(x)*(1-p)^(n-x)dx

I am unable to proceed beyond this point. Can somebody help me here? What would be the final solution for this if we apply limits (0,n)?

Thanks,
Sivaram.

2. Originally Posted by Sivaram
Hi,

I am trying to integrate the following

Integral of x*n!/x!(n-x)! *p^(x)*(1-p)^(n-x)dx limits being (x=0,n)

I applied the rule of integration by parts as follows -

Let u = x & dv = n!/x!(n-x)!*p^(x)*(1-p)^(n-x)dx

Therefore, du=dx
V= integral n!/x!(n-x!)*p^(x)*(1-p)^(n-x)dx

I am unable to proceed beyond this point. Can somebody help me here? What would be the final solution for this if we apply limits (0,n)?

Thanks,
Sivaram.
First try replacing the factorials with appropriate gamma functions (factorial
is only defined for non-negative integers, you need something defined for all
reals in (0,n). Alternatively replace the integral with a summation from 0 to
n, which is 1 as you are summing the binomial distribution with parameters
n, p over all possible outcomes.

If the latter is the case, your original sum would heve been the mean of the
binomial distribution with probability of success on a single trial of p, and
a total of n trials, this is n*p.

RonL

RonL