(Solved): 5. An auto insurance claim has the distribution function of a discrete random variable X has th ...

5. An auto insurance claim has the distribution function of a discrete random variable $\mathrm{X}$ has the distribution function is given by $F(x)=?\begin{array}{cc}0,& x<?2\\ 0.2,& ?2?x<0\\ 0.5,& 0?x<2.2\\ 0.6,& 2.2?x<3\\ 0.6+q,& 3?x<4\\ 1,& x?4\end{array}$ Suppose that $\mathrm{Pr}(\mathrm{X}>3)=0.1$ : (a) Determine the value of $q$ ? (b) Compute $\mathrm{Pr}\left({\mathrm{X}}^2>2\right)$ : (c) Find $p(0);p(1)$ and $p(\mathrm{Pr}(X?0))$ : (d) Find the formula of the probability mass function $p(x)$. (c) Compute E(X):