1. The lifetime, X, of a CPU in the Edsel computer, measured in months, has the following probability density function: f(x)= 338 x3 for x ≥ 13 and 0 otherwise. a) What is the probability that an Edsel CPU lasts at least two years? b) What is the probability that X < 15? c) What is the probability that 13< X < 20?
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!
1. The lifetime, X, of a CPU in the Edsel computer, measured in months, has the following
f(x)=
| 338 |
| x3 |
for
and 0 otherwise.
a) What is the probability that an Edsel CPU lasts at least two years?
b) What is the probability that X < 15?
c) What is the probability that 13< X < 20?
d) What is the
e) What is the expected value of X - 7?
f) What is the expected value of 3X?
g) What is the expected value of
| 1 |
| X |
?
h) What is the probability that X is less than its expected value?
i) What is the expected value of
| X |
?
j) What is the 50th percentile of X?
k) What is the probability that X is within 1 standard deviation of its expected value?
l) What is the probability that X = 15?
m) Add any comments into the text box here.
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