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
a) find the value of k that will make f(x) a valid probability density function
b) sketch the curve of f(x)
c) find P(1<X<3)
d) find the cumulative distribution function F(X). for x
e) find the expected value of X
f) 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/20/let-x-be-a-continuous-random-variable-whose-probabilily-dens-1044179-1761542913-0.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")
