A) Kích thước một quần thể y(t) tăng theo thời gian t mô hình bởi phương trình vi phân dy = k(M – y) với k, M là các hằng số dương và y(0) = y, (kích thước ban đầu quần thể là y,). dt Giải phương trình tìm y(t) và ước tính giá trị của y(t) sau khoảng thời gian t đủ lớn (tính theo các hằng số k, M,y,) b) Giải phương trình sai phân: y,+2 +2y,+1+2y, =24

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?