2 = 2 = 1x2 ————————————
2+4 = 6 = 2x3
————————————
2+4+6 = 12 = 3x4
————————————-
2+4+6+8 = 20 = 4x5
————————————-
2+4+6+8+10 = 30 = 5x6
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Look at the table. Make a conjecture about the sum of the first 30 positive even numbers.
A: The sum is 29 x 30
B: The sum is 31 x 32
C: The sum is 30 x 30
D: The sum is 30 x 31

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?