Let x be a fair dice roll, that is a sample from the uniform distribution in f1; 2; : : : ; 6g. let y be the number of heads in x tosses of a fair coin, that is a coin which is landing heads with probability 1 2 and tails otherwise. we assume the outcome of each coin toss is independent from the outcome of the other coin tosses and from x. a. compute e(y jx = x) for any x = 1; 2; : : : ; 6. b. prove that e(y ) = 1 2 e(x) (1) and derive the value of e(y ). explain intuitively why (1) makes sense.

The avenues in a particular city run north to south and are numbered consecutively with 1st avenue at the western border of the city. the streets in the city run east to west and are numbered consecutively with 1st street at the southern border of the city. for a festival, the city is not allowing cars to park in a rectangular region bordered by 5th avenue to the west. 9th avenue to the east, 4th street to the south, and 6th street to the north. if x is the avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park? 5th ave 9th ave

The diagram represents the polynomial 4x2 + 23x – 72. what is the factored form of 4x2 + 23x – 72? (4x + 8)(x – 9) (4x – 8)(x + 9) (4x + 9)(x – 8) (4x – 9)(x + 8)

The length of a field is 100 yards and its width is 75 yards. if 1 inch represents 25 yards, what would be the dimensions of the field drawn on a sheet of paper?