### Continuous distribution

1. Let the random variable X have the p.d.f. f(x)=2(1-x) for 0<x<1 and zero elsewhere. a. Sketch the graph b. Determine and sketch the graph of the distribution function of X c. find P(X) for the following intervals: i. [0,1/2] ii. [1/4,3/4] iii. X=3/4 iv. X>3/4 2. For each of the following functi