Caitlin invested in a lifetime annuity that begins payments at age 65. Her life expectancy is 88. Caitlin invested $1,000,000 in the annuity, which earns 4.1% APR, compounded monthly. With this annuity, what is Caitlin's monthly payment amount? A. $3907.93
B. $4100.00
C. $5601.87
D. $5432.86

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?