Let x and y be independent binomial random variables having parameters (n, p) and (m, p), respectively. let z = x + y.
(a) argue that z has a binomial distribution with parameters (n + m, p) by writing x and y as appropriate sums of bernoulli random variables.
(b) validate the result in (a) by evaluating the necessary convolution.

Use the matrix-column representation of the product to write each column of ab as a linear combination of the columns of a.

Drag the tiles to the correct boxes to complete the pairs. match the cart-coordinates with their corresponding pairs of y-coordinates of the unit circle

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem