The amount of time (in minutes) that an executive ofa certain firm talks on the telephone is a random variablehaving the probability density f(x) =⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩x4for 0 < x F 24x3 for x > 20 elsewhere With reference to part (b) of Exercise 60, find theexpected length of one of these telephone conversationsthat has lasted at least 1 minute.
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 certain firm talks on the telephone is a random variable
having the probability density
⎧
⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎩
x
4
for 0 < x F 2
4
x3 for x > 2
0 elsewhere
expected length of one of these telephone conversations
that has lasted at least 1 minute.
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