What is the standard form of the following equation:
y = 2x^2 - 10x + 6
a) y = 2(x - 2.5)^2 - 6.5
b) y = (x - 5)^2 - 12.5
c) y = 2(x + 6.25)^2 + 6
d) y = 2(x - 2.5)^2 + 6

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?