t is known to show an exponential distribution where the average lifespan of a type of CPU is nine years. What is the probability that the company

The lifetime, in years, of a certain type of electrical switch has an exponential distribution withan average lifetime of 2 years. Question. For a single system, what is the probability we can keep one switching mechanismoperable for 10 years if we assume we can replace a switch due to failures up to three timesduring the 10-year period?

DLP projectors are used in the majority of cinema projection systems and require a special light bulb to display a picture. Assume that the average life of a DLP bulb is 2,000 hours and that this failure time follows the exponential distribution. Answer the following questions, performing all computations with Excel functions.

An October 26, 2020 news report raised alarms that the population of North Atlantic Right Whales had declined a dramatic 11% with increased risk for the whales extinction in the near future. Whale deaths are largely caused by collisions with fishing boats and by whale entanglement in fishing nets and lobster trap gear.  “Since the population peaked at 481 whales in 2011, there have been 103 births, but roughly 218 whales have died, presumably because of human activity – a rate of 24 deaths per year.”  Subtracting births from death, what is the yearly net decrease in the Right Whale population between 2011 and 2020?  Create a linear mathematical model for the decline in Right Whale population since 2011 (i.e. let 2011 be year zero).  The article says that in 2018 there were 366 Right Whales counted.  How accurate is your linear model when compared to the 2018 whale count?