The diameter , Say X , of a electric cable , is assumed to be continuous random variable with p.d.f : f(x)= 6x(1-x) , 0<=x<=1.

(1) Check that the above is a P.D.F.

(2) Obtain an expression for the c. d. f. of X.

(3) Compute P(X<=1/2| 1/3<=X<=2/3), and

(4) Determine the value of k such that P(X<k)=P(X>k).

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5. The diameter, say X of an electric cable, is assumed to be a continuous random

variable with p.d.f : f(x)=6x(1-x), , 0≤x≤1

1) Check that the above is p.d.f.,

2) Obtain an expression for the p.d.f

3) Compute P(X≤1/2 | 1/3≤X≤2/3), and

4) Determine the number k such that P(Xk)

6. Let X be a random Variable with following probability distribution