show work please

3. (23 points) On the Swamp County Railroad system there are 6 types of train Pl P2 P3 FI F2 F3 They occur with the following probabilities P1 0.05 P2 0.10 P3 0.15 F2 0.15 A trackside device transmits the type of train that passes. (a) (3 points) If a fixed-length code is used, how many bits need to be sent for each train? (b) (12 points) Given the probabilities above, devise a Huffiman code and fill in the following table Symbol Code P1 P2 P3 F1 F2 F3 (c) (5 points). What is the AWCL of your answer to (b)? (d) (3 points). If 1000 trains pass, with the distribution shown, how many bits are saved by using the Huffiman code instead of the fixed code from (a). Show your calculations