Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding a combination discrete and continuous cdf to make a new cdf

  1. Jul 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Let F(x)[itex]=\begin{cases}
    .25e^{x} & -\infty<x<0\\
    .5 & 0\leq x\leq1\\
    1-e^{-x} & 1<x<\infty\end{cases}$. Find a CDF of discrete type, F_d(x) and of continuous type, F_c(x) and a number 0<a<1 such that F(x)=aF_d(x)+(1-a)F_c(x)

    2. Relevant equations

    3. The attempt at a solution
    don't really have any idea of where to begin. i have the answers in the book. any hint would be greatly appreciated.
  2. jcsd
  3. Jul 1, 2011 #2


    User Avatar
    Homework Helper

    fc will be continuous, but still will need to be defined explicitly for each interval

    use the discrete probabilities to account for the discontinuities in the current function at x=0,1
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook