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(Solved): how do you answer  1. Let \( X \) be a continuous random variable with the following probabilit ...



how do you answer 

1. Let \( X \) be a continuous random variable with the following probability density function:
\[
f(x)=\left\{\begin{array}{
1. Let \( X \) be a continuous random variable with the following probability density function: \[ f(x)=\left\{\begin{array}{cc} 2(x-1) & 11.5) \). e. Find the moment generating function, MGF, for \( X \) f. Find the expected value and standard deviation for \( X \).


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a) R-code : > x<-seq(0,1,by=0.01) > x1<-seq(0,1,by=0.01) > x2<-seq(1,2,by=0.01) > x3<-seq(2,3,by=0.01) > y1<-rep(0,length(x1)) > y2<-2*(x2-1)
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