(Solved): f(x)={kx200<x<1elsewhere Find the value k and the probability that the random vari ...

$$f(x)=\{\begin{array}{ll}k{x}^2& 0<x<1\\ 0& \text{ elsewhere }\end{array}$$ Find the value $$k$$ and the probability that the random variable takes on a value (a) between $$\frac{1}{4}$$ and $$\frac{3}{4}$$. (b) greater than $$\frac{2}{3}$$. (c) Find the expectation of $$X$$. (d) Find the variance of $$X$$. (e) When $$X$$ is known to be located between $$\frac{1}{4}$$ and $$\frac{3}{4}$$, what is the probability that $$X$$ is greater than $$\frac{2}{3}$$ ?