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 April 20th, 2018, 01:01 AM #1 Member   Joined: Jan 2016 From: Blackpool Posts: 95 Thanks: 2 Cumulative function question A random variable has a cumulative distribution function $F_{X}(x)=c+de^{\frac{-x^2}{2}}$ if x>0 and 0 otherwise, what values must c and d have to make this a valid pdf?
 April 23rd, 2018, 07:08 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,194 Thanks: 871 The "cumulative probability function", $\displaystyle F_X(x)$, gives the probability that x< X. Now, you are told that the probability that x is negative is 0 so what is the probability that x< 0? What is $\displaystyle F_X(0)$ by this formula? Set those equal. Further, the total cumulative probability is 1. What is the limit of $\displaystyle F_X(x)$ as x goes to infinity? Set that equal to 1. Now you have two equations to solve for p and q. Thanks from Jaket1
 April 23rd, 2018, 12:20 PM #3 Global Moderator   Joined: May 2007 Posts: 6,527 Thanks: 588 $F_X(\infty)=c=1,\ F_X(0)=c+d=0$

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