Let X denote the temperature at which a certain chemical
136. Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has pdf
The authors propose the values a = 150  and
b = 90. Assume this to be the correct model.
a.   What is the probability that the depth of the deepest pit is at most 150? At most 300? Be- tween 150 and 300?
b.   Below what value will the depth of the maximum pit be observed in 90% of all such experiments?
c.    What is the density function of X?
d.   The density function can be shown to be uni- modal (a single peak). Above what value on the
1Â Â Â Â Â Â Â Â Â Â 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â measurement axis does this peak occur? Â (This
f 1x 2 = • 914 - x  2   -1 x 2
0Â Â Â Â Â Â Â Â Â Â Â otherwise
a.    Sketch the graph of f(x).
b.   Determine the cdf and sketch it.
value is the mode.)
e. It can be shown that E(X) = .5772b + a. What is the mean for the given values of a and b, and how does it compare to the median and mode? Sketch the graph of the density function.(Note: This is called the largest extreme value distribution.)
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Posted 07 May 2017 05:05 PM
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