3 . The proportion of salt* left in the salt shakers at the end of the day at a crowded restaurant has a probability density function given by f ( x

The proportion of salt X left in the salt shakers at the end of the day at a crowded

restaurant has a probability density function given by

3 . The proportion of salt* left in the salt shakers at the end of the day at a crowdedrestaurant has a probability density function given byf ( x ) = ]2xfor Dex= ]Ootherwisea ) There are 100 salt shakers in the restaurant with each one having a capacity of 2ounces of salt and they are all filled independently of each other .1 ) ( 1. 5 points ) What is the expectation of I = the total amount of salt needed tofill the 100 salt shakers at the end of the day ?1 1 ) ( 1.5 points ) What is the variance of ! ?b ) ( 2 points ) What is the pdf of { = the maximum proportion of salt amongst the 100 saltshakers ?"