Question: -Explain why the following functions are, or are not, probability density functions: a)f(x)= x 2 f o r x [ 1 , x ] (b)

-Explain why the following functions are, or are not, probability density functions:

a)f(x)=x2forx[1,x] (b) f(x)=5(9x2x4) for x[0,3]

-Find the probability P (x 23 ) given the probability density function you identi- fied in Question a and b. Give an exact answer, and an approximate answer to two decimal places.

-Why is Property 1 in Question a and b essential for a function to be a probability density function?

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