1.Let X be a continuous random variable with the probability density function f(x)=k \cdot \sqrt{x}, \quad 0 \leq x \leq 4 \begin{aligned} & f(x)=0, \\ & \text{^^20otherwise.^^20}\end{aligned} a)What must the

value of k be so that f(x) is a probability density function? b)Find the cumulative distribution function of X, Fx(x)=P(X<=x). c)Find the probability P(1<= X <=2). d)Find the median of the distribution of X. That is, find m such that P(X<=m)=P(X >=m) =½. e) Find the 30th percentile of the distribution of X. \text { g) Find } \sigma_{X}=\operatorname{SD}(X) \text { . } \text { f) Find } \mu_{X}=E(X) \text { . }