Continuous random variable

The mode of a continuous random variable X is 1 and this is a stationary point. Given that X takes values over the range [0, 3] find possible expression for:
(a) the c.d.f. of X
(b) the p.d.f. of X.
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How could I find them?

Quote:

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Originally Posted by geton

The mode of a continuous random variable X is 1 and this is a stationary point. Given that X takes values over the range [0, 3] find possible expression for:
(a) the c.d.f. of X
(b) the p.d.f. of X.
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How could I find them?

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Try letting the pdf be a cubic in x, with roots at x=0 and x=3, and a local maximum at x=1. Then normalise so that the integral from 0 to 3 is equal to 1.

Then so long as the third root is not in the open interval (0,3) you have a pdf satisfying the given conditions, and from that you should be able to find the cdf.

CB