The following is the p.d.g. (Probability Density Function) of a continuous random varible X: `f(x)=(x)/(32), 0ltxlt8 =0,` otherwise (a) Find following the expression for c.d.f. (Cumulative Distribution Function) of X. (b) Also find its value at `x=0.5 and 9.`

The following is the p.d.g. (Probability Density Function) of a contin

1.	The following is the p.d.g. (Probability Density Function) of a continuous random varible X: `f(x)=(x)/(32), 0ltxlt8 =0,` otherwise (a) Find following the expression for c.d.f. (Cumulative Distribution Function) of X. (b) Also find its value at `x=0.5 and 9.`
Answer» (a) c.d.f. of a continous random variable X is given by `f(x)=underset(-oo)overset(x)intf(y)dy` `therefore f(x)=underset(0)overset(x)intf(y)dy=underset(0)overset(x)int(y)/(32)dy` `=[(y^(2))/(64)]_(0)^(x)=(x^(2))/(64)` Thus , `F(x)=(x^(2))/(64),x inR.` (b) Values of `F(x)` at different values of x. At `x=0.5,F(x)=F(0.5)=((0.5)^(2))/(64)=(0.25)/(64)=(1)/(256)` For any value ofx greater than or equal to `8.F(x)=1` `therefore F(9)=1`