Homework SourseLet X be a continuous random variable whose probabilily dens
Let X be a continuous random variable whose probabilily density funtion is one of the form
f(x)= kx for 0<=x<=2 ], k(4-x) for 2<x<=4 , and 0 otherwise
We know that a value of k that makes the function valid is k=1/2
a) find P(1<X<3)
b) find the cumulative distribution function F(X). for x
c) find the expected value of X
d) Find the Variance of X
Solution
![Let X be a continuous random variable whose probabilily density funtion is one of the form f(x)= kx for 0<=x<=2 ], k(4-x) for 2<x<=4 , and 0 otherwi](/WebImages/6/let-x-be-a-continuous-random-variable-whose-probabilily-dens-986725-1761506997-0.webp "Let X be a continuous random variable whose probabilily density funtion is one of the form f(x)= kx for 0<=x<=2 ], k(4-x) for 2<x<=4 , and 0 otherwi")
