A consumer is contemplating the purchase of a new smart phone. A consumer magazine reports data on the major brands.Brand A has lifetime (TA),which is exponentially distributed with m=0.2;and Brand B has lifetime (TB),which is exponentially distributed with m = 0.1 (The unit of time is one year) a. Find the expected lifetimes for A and B. If a consumer must choose between the two on the basis of maximizing expected lifetime, which on should be chosed? b.Find the probability that A's lifetime exceeds its expected value.Do the same for B. What do you conclude? c.Suppose one consumer purchases Brand A, and another purchases Brand B.Find the mean and variance of 1) the average lifetime of the two devices and 2) the difference between their lifetimes.(Hint:You must use the rules about means and variances of linear transformations discussed in Chapter 7. Making Hard Decision with decisiontools,3rd edition)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A consumer is contemplating the purchase of a new smart phone. A consumer magazine reports data on the major brands.Brand A has lifetime (TA),which is exponentially distributed with m=0.2;and Brand B has lifetime (TB),which is exponentially distributed with m = 0.1 (The unit of time is one year)
a. Find the expected lifetimes for A and B. If a consumer must choose between the two on the basis of maximizing expected lifetime, which on should be chosed?
b.Find the probability that A's lifetime exceeds its expected value.Do the same for B. What do you conclude?
c.Suppose one consumer purchases Brand A, and another purchases Brand B.Find the mean and variance of 1) the average lifetime of the two devices and 2) the difference between their lifetimes.(Hint:You must use the rules about means and variances of linear transformations discussed in Chapter 7. Making Hard Decision with decisiontools,3rd edition)
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