Let x take value between 0 and 3. x is a continuous random variable .pdf

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Let x take value between 0 and 3. x is a continuous random variable with the following density, f(x)=cx2. a) for f(x) to be a valid density what must c equal? b) find e(x) c) find var(x) d) find p(1_x_3) e) find p(1 Solution a)f(x)=cx^2; we know that integration of 0 to 3 of f(x)dx=1; after simplyfying we get 9c=1; =>c=1/9; b)mean=integration 0 to 3 of x*f(x)dx; mean=9/4; c)variance=27/80; d)p(1.

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