107. Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has pdf f(x)


1 9

(4  x2

) 1  x  2 0 otherwise

a. Sketch the graph of f(x).

b. Determine the cdf and sketch it.

c. Is 0 the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than 0?

d. Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let Y
the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? (Give the name and values of any parameters.)