1) Let X have the p.d.f f(x) = 3(1-x)2, 0≤x<1. Compute:
a) P(0.1 < X < 0.5)
2) Find the mean and variance, and determine the 90th percentile , of each of the distributions given by the following densities:
a) f(x) 2x, 0≤0<0
3) Find the 50th percentile ( median ), the 25th percentile ( first quartile ), the 75th percentile ( third quartile ), and the 90th percentile ( also called the ninth decile ) for the following densities:
a)4x3 , 0≤x<1
Consider the uniform ( rectangular ) distribution on the space [a,b), where a<b, with p.d.f
f(x) 1/b-a' a≤x<b
a) Obtain the cumulative distribution function F(x). Determine the median and the first and third quartiles, and calculate the mean and variance.
I really just need to know which formulas I use here. The book has several pages deriving formulas, I can't see the wood for the trees.