# Homework Help: Variance in Statistics

1. Sep 21, 2005

OK, I am having no problem with the concepts here but just with a particular problem. I have analyzed this problem to bits and nothing is working. Here is what we have:

The bending capabilities of plastic sheets are investigated by bending sheets at increasingly large angles until a deformity appears in the sheet. The angle x at which the deformity first appears is then recorded. Suppose that this angle takes values between 0 degrees and 10 degrees with a probability density function:

f(x) = A(e^(10-x)-1)

for 0 <= x <= 10 and f(x) = 0 elsewhere.

a. Find the value of A.
b. Find the cumulative distribution function.
c. What is the variance of the deformity angle?
d. Find the upper and lower quartiles.

To get A, we say:

Integral of Probability Density Function from -Infinity to Infinity = 1
A ends up being (e^(10)-11)^-1

Cumulative Distribution Function is:

Integral of PDF from -Infinity to x which is:

(e^(10)-11)^-1*(-e^(10-x)-x+e^10)

Variance is E(x^2) - E(x)^2, which I end up getting .984911577 for the Variance.

Now, for the last part here, I just cannot solve the equation. It goes like:

Cumulative Distribution Function = p

So...

(e^(10)-11)^-1*(-e^(10-x)-x+e^10) = p

I cannot solve for x here. Can anyone here do this? Or is my CDF wrong or something? Thanks for any help. I am absolutely stumped here after checking over my work several times.