please help me with step by step calculation

2.1 Solve the below problem (show all calculations). Let Y, and Yz be random variables with joint density function f ( y1 12) ) = . elsewhere. 2.1.1 Find the marginal density function of f()1) and f(12). (2.5+2.5=5) 2.2.2 Find E(V1) and V(Y]) [Hint. You may also identify the distributions of the marginal density functions and use it to find the E (Y]) and V(Y] )]. (2+2=4) 2.2 Solve the below problem (3) Table 1 contains the probabilities associated with each possible pair of values for Y, and Yz and is known as the joint probability function for Y, and Y, Table: Probability function for Y, and Y, V1 2 0 1 2 0 1/9 2/9 1/9 1 2/9 2/9 0 2 1/9 0 0 Find F (1, -1), F (1.5, 2), and F (2,2). 2.3 Solve the below problem. (5) Caltex petrol is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Consider the joint density of Y), the proportion of the capacity of the tank that is stocked at the beginning of the week and Y2, the proportion of the capacity sold during the week, given by [3yr f (> >=) = 10, elsewhere. In each week an average of 75% of the petrol is sold and an average of 37.5% of the petrol remains in the Caltex bulk tank at the end of each week. 2.3.1 Due to the COVID pandemic and South African lockdown level 5 rules (with many citizens working from home), the Caltex petrol station had one week where they did not sell any petrol. If no petrol was sold in this particular week, find E( Y1 - Y2), which denotes the proportion of petrol remaining at the end of the given week. (Show your calculations) (3) 2.3.2 In any given week of the year, what is the probability that that the amount of petrol sold during the week is more than the amount of petrol that was stocked in the beginning of the week ? (