- #1

bodycare

- 10

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- TL;DR Summary
- Simple statistics and calc problem. Given two boundary conditions of a cdf how does one find the interval of the cdf.

I'm not quite sure if my problem is considered a calculus problem or a statistics problem, but I believe it to be a statistics related problem. Below is a screenshot of what I'm dealing with.

For a) I expressed f(t) in terms of parameters p and u, and I got: $$f(t)=\frac{-u \cdot a + u \cdot b + a}{(\frac{1}{p \cdot(p-1)}+\frac{1}{p}+u \cdot a - u \cdot b - a)\cdot(\frac{1}{p \cdot (p-1)}+\frac{1}{p})} $$

I am unsure how to use this to find the values for a and b. I assume (hence my post in the stats forum) that I need to use the fact that f(t) is a cdf. I was thinking that since f(t) is a cdf that f(0)=0 and f(D)=M, since 0 work would be done at time t=0 and all the work would be done after D days, but this is just a thought. I need with finding the values a and b which I believe will set me up for solving b).

For a) I expressed f(t) in terms of parameters p and u, and I got: $$f(t)=\frac{-u \cdot a + u \cdot b + a}{(\frac{1}{p \cdot(p-1)}+\frac{1}{p}+u \cdot a - u \cdot b - a)\cdot(\frac{1}{p \cdot (p-1)}+\frac{1}{p})} $$

I am unsure how to use this to find the values for a and b. I assume (hence my post in the stats forum) that I need to use the fact that f(t) is a cdf. I was thinking that since f(t) is a cdf that f(0)=0 and f(D)=M, since 0 work would be done at time t=0 and all the work would be done after D days, but this is just a thought. I need with finding the values a and b which I believe will set me up for solving b).