please answer all the questions

To create vector Y where Y = minimum(X1, X2, X3) we can use: >>Y=min(X1,min(X2,X3)); % Produces vector: Y = [y;] = [min (x1;, x2;, x3;)] Note that Y is a discrete RV (possible values 0,1,2,..., 20). We estimate py (y) = P(Y = y) by the sample proportion of times Y =y. Create a normalized histogram of Y. \"normalized\" for a discrete random variable means to express the column height as proportions (note the proportions must naturally sum to 1; a requirement for any pmf) Use the appropriate number of bins so that the columns align with the integer values. You may have to try a couple until you get something you like. Promising candidates include: >>bins=21; % (one bin for each integer 0,1,2,...,20), but this might not space the columns quite right if the min(Y) > O or the max(Y) >bins=max(Y)-min(Y)+1; To create the normalized histogram you can use: >> histogram(Y,bins, 'normalization', 'probability\") Note: To normalize a discrete RV (as in this case) use 'probability'. To normalize a continuous RV (as you did in Homework#3) use 'pdf'. In addition, compute the mean and standard deviation o_f Y; the commands are mean(Y) and std(Y) respectively. Note these would be denoted Y and sy respectively since they are based only on our sample results they are estimates of uy and oy respectively. For you to hand in: a. normalized histogram of Y b. mean and standard deviation of vector Y G Based on your simulation estimate P(Y >Prob=(sum(Y