Illustration 9.22. Calculate the GM of the data given in the first two columns Table 9.19.
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- b) Explain how X can be related to the exponential distribution by using a moment generating function argument.Suppose that the length of a phone call in minutes follows exponential distribution with parameter λ=8. If some one comes ahead of you in queue of telephone booth, then find the probability that you have to wait between 10 and 20 minutes.Suppose that the length of long distance phone calls, mea- sured in minutes, is known to have an exponential distribution with the average length of a call equal to 15 minutes. Find the CDF.
- Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to $18 minutes. The lambda of this distribution is The probability that the length of a phone call is longer than 22 is P(x ≥ 22) = The probability that the length of a phone call is shorter than 12 is P(x ≤ 12) =Suppose that Steph Curry's cumulative free throw percentage, one month into the NBA season, is below 80%, but that one game later it is above 80%. Did there have to be a moment where his cumulative free throw percentage was exactly 80%? If no, give a simple numerical example showing how this might fail to happen. If yes, explain why there must have been such a moment.Suppose that the first Section of Applied Stat class ends at 13:20 and the second starts at 13:30 with ten minutes break. Professor, who teaches both sections, wants to go to bathroom during the break. Suppose that the time that takes for professor to go to bathroom and come back to the classroom has an exponential distribution with the mean of 6.7 minutes. Find the probability that the professor will be late for class for less than 3 minutes (round to 3 decimal places).
- A random sample of size n = 225 is to be taken from an exponential population with θ = 4. Based on the cen-tral limit theorem, what is the probability that the mean of the sample will exceed 4.5?show geometric distributions belong to exponential classSuppose the time until your iPhone breaks is uniformly distributed between 0 and 8 years. You will get a new phone as soon as your iPhone breaks or at time 2 (when a new iPhone is released), whichever is first. Find the standard deviation for the time until you get a new phone.1. 0.622. 0.553. 0.494. 0.525. 0.57
- Suppose that during rainy season on a tropical island the length of theshower has an exponential distribution, with parameter λ = 2, time beingmeasured in minutes. What is the probability that a shower will last morethan three minutes? If a shower has already lasted for 2 minutes, what is theprobability that it will last for at least one more minute?suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.6 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 8.6 secons. What would you use for the alternative hypothesis?A microprocessor that controls the tuner in color TVs fails completely at random (that is, according to the exponential distribution). Suppose that the likelihood that a microprocessor that has survived for k years fails in year k + 1 is .0036. What is the cumulative distribution function of the time until failure of the microprocessor?