(3) The distribution of a random variable X which has possible values 1 to 4 involves an unknown parameter 9. 1P(X=1)=0.19 1P(X=2)=0.26 IP(X=3)=0.329 1P(X=4) =0.4+49 Let X1, X2, . . . , Xn be independent and identically distributed, each with the same distribu- tion as X described above. Let X be the sample mean, that is, X 2 (X1 +X2 |. . .+Xn)/'n,. (a) [2pts] What is the possible range for 0 to make the given distribution reasonable? In other words, what is the range of 6 that makes any given probability be between 0 and 1'? (b) [2pts What is E(X1)? (c) [1pt] What is E(X)