(a) ( 4 points) The density function of a random variable ( X ) is given by [ f(x)=left{egin{array}{ll} p+q x^{2}, & ext { for } 0 leq x leq 1 \ 0, & ext { otherwise } end{array} ight. ] If ( mathrm{E}(X)=0.6 ), find ( p ) and ( q ). (b) Suppose that ( Y ) follows a Poisson distribution. (i) (2 points) If ( operatorname{Pr}(Y=0)=operatorname{Pr}(Y=1) ), determine ( mathrm{E}(Y) ). (ii) (2 points) If ( operatorname{Pr}(Y=1)=operatorname{Pr}(Y=2) ), determine ( mathrm{E}left(Y^{2} ight) ). (c) (3 points) Suppose that ( Z ) follows a standard normal distribution, determine ( operatorname{Pr}(Z>-0.56 mid Z

(a) ( 4 points) The density function of a random variable X is given by f(x)={p+qx2,0,for0x1otherwise. If E(X)=0.6, find p and q. (b) Suppose that Y follows a Poisson distribution. (i) (2 points) If Pr(Y=0)=Pr(Y=1), determine E(Y). (ii) (2 points) If Pr(Y=1)=Pr(Y=2), determine E(Y2). I (c) (3 points) Suppose that Z follows a standard normal distribution, determine Pr(Z>0.56Z