Go to the website wolframalpha. com and enter: "integrate." follow the instructions and use them along with the improved estimate to verify the fair price for 140 units of about $21 million given in the text. then enter "sum" into wolframl alpha and follow the instructions to verify the fair price by summing the first 140 values of c(n). discuss how the solution compares with the solutions provided by the integration and summation features on a graphing calculator, as well as the solution provided by adding up the values using a spreadsheet.

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?