(Solved): 1. Let X be a continuous random variable whose probability density function is f(x)={4x300 ...
1. Let X be a continuous random variable whose probability density function is f(x)={4x3?0?0?x?c otherwise ? What is the value of c that makes f(x) a valid probability density function (PDF). 2. Let f(x)={0.048x(5?x)0?0?x?5 otherwise ? (a) Verify that f is a probability density function. (b) Find P(X?4). 3. Sketch the region bounded by the given curves, and then find the area of the region. (a) y=x2?x,y=3?x2 (b) y2=x,4y?y2=x