Lucas took an express train into the city last weekend without any stops. He boarded the train at 9:30 a. m. and arrived in the city at 11:15 a. m. The train’s average speed was 60 miles per hour. How far did Lucas travel by train?

The discrete random variables x and y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 tabulate the distribution and show that a = 0.1.2 find the marginal distributions of x and y. 3 calculate cov(x,y).4 state, giving a reason, whether x and y are independent. 5 calculate e(y|x = 1).