Question 1185097


1.  {{{p + 2p + 3p  +4p = 10p = 1}}}  ===> {{{p=1/10}}}


2.  {{{E(X) = sum(x[i]*p(x[i]), i=1,4) = 1*(1/10)+2*(2/10)+3*(3/10)+4*(4/10) = (1/10)*(1+4+9+16) = 30/10 = 3}}}


3.  Your formula for variance is wrong -- it should be {{{Var(X) = E(X^2)- (E(X))^2}}}.

Now {{{E(X^2) = sum(x[i]^2*p(x[i]), i=1,4) = 1*(1/10)+4*(2/10)+9*(3/10)+16*(4/10) = (1/10)*(1+8+27+64) = 100/10 = 10}}}


===> {{{Var(X) = 10 - 3^2 = 1}}}