Math Help - p.d.f mean

1. p.d.f mean

Compute an approximate probability that the mean of a random variable sample of size 15 from s distribution with p.d.f

f(x)=3x^2 0<x<1

f(x)=0 elsewhere,

is between 3/5 and 4/5.

2. Originally Posted by varkoume.com
Compute an approximate probability that the mean of a random variable sample of size 15 from s distribution with p.d.f

f(x)=3x^2 0<x<1

f(x)=0 elsewhere,

is between 3/5 and 4/5.

Provided the sample size is sufficiently large, the distribution of the sample mean is approximately normal (regardless of the parent population distribution) with mean equal to the mean of the underlying parent population and variance equal to the variance of the underlying parent population divided by the sample size.

I wouldn't have thought that n = 15 was very large, but the above is probably what you're expected to apply.

3. I am sorry this is not help me ;/

4. Originally Posted by varkoume.com
I am sorry this is not help me ;/
Start by calculating the man and variance of X using the given pdf. You can do that, right?

Then the sample mean is (very) roughly distributed as a normal distribution with mean as above and variance as above but divided by n (15 in this case).