The student ID is 3124785

Precomputation: Label the last 6 of your Student ID starting from the 2nd digit as a, b, c, d, e,f (if your ID is 3124785, then a=1,b=2,..,e=8,f=5). Let t=a+b+c+d+e+f. Define the joint distribution for (X, Y) where p(i,j)=Pr[X=i, Y=j] by p(1,-1)=a/t p(1,0)=b/t p(1,1)=c/t p(3,-1)=d/t p(3,0)=e/t p(3,1)=f/t Calculate the following with full justification (a) E[YIX=1] (b) E (c) E[X] (d) What is the best guess for X, given Y=0? What is the probability of error when making this guess? (e) What is the best guess for Y, given X=3? What is the probability of error when making this guess? (f) Which guess is harder? The one in (e) or in (f)? Explain. (g) Write down the joint distribution that would result, in an array similar to the one given, when X and Y have the marginal distributions in the example above and X and Y are independent