Question: Let X be a continuous random variable whose probability density function is fx 2 3 2 9 x 0 x 3 0 otherwise

Let X be a continuous random variable whose probability density function is fðxÞ ¼

2 3  2 9 x 0 x 3 0 otherwise

(a) Sketch the probability density function f(x). Is the area under the curve equal to one?

(b) Geometrically calculate the probability that X falls between 0 and ½.

(c) Geometrically calculate the probability that X falls between ¼ and 3

/4.

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