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3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0...

3. Let X be a continuous random variable with PDF

fX(x) = c / x^1/2, 0 < x < 1.

(a) Find the value of c such that fX(x) is indeed a PDF. Is this PDF bounded?

(b) Determine and sketch the graph of the CDF of X.

(c) Compute each of the following:

(i) P(X > 0.5).

(ii) P(X = 0).

(ii) The median of X.

(ii) The mean of X.

Math   Statistics-And-Probability   
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