Question

A farmer knows from experience that his wheat harvest  Q (in       

                     bushels) has the probability distribution given by:

                                         Q = 150  with probability  0.30 ,

                                              = 170    with probability  0.45,

                                               =200    with probability  0.25;

                      note that the probabilities add up to 1 as they are required by a probability   

                      distribution. Suppose the demand function he faces in the market place is given by:

                                              p  =  320  -  0.5  Q

                       where  p =  price in dollars per bushel. Let  R  = total revenue = p x Q. [Note: You may find it

                      convenient to first derive the probability distribution of  R.]

                     (i) (6 points). Find E ( R ).

                      Also, define his Profits as :

                                            Profits =  R - C  ,

                     where the total cost  C  (in dollars) is a function of  Q  given by

                                            C =  150  -   10 Q   + 2 Q².

                      (ii) ( 9 points). Find  E(Profits).

                (d)  ( 6 points).Suppose you know the values  of  : Mean = E ( X )  and  Variance = V(X)  of a   

                      variable  X  in a given population. Indicate how you will construct T₁    and  T₂  such that

                                               P( T₁  <   X_f    < T₂  )   =  0.9  (approximately),

where  X­_f    is the value of  X  you will observe on the individual you will draw randomly from the population. Assume that you know  X₀  ≠  X_f  , which is a realized value of  X. [Do not assume that X is normal.]

Answer 1

i tried my best ,i hope it ill help u please give thums up thank u