Let the Continuous Random Variable X Have the Density Function Fx X as Shown in the Figure Below

Let X be a continuous random variable, with density fx(x). We denote by Fy its cumulative...

Let X be a continuous random variable, with density fx(x). We denote by Fy its cumulative distribution function.

(i) Let Y1 = 3X + 2. Express the cumulative distribution function of Yi in terms of Fx. What is the density of Yi, in terms of fx (hint: the density of a r.v. can be recovered as the derivative of its cumulative distribution function)?

(ii) Let Y2 = 1 - X. Find its cumulative distribution function and its density, in terms of Fx and fx

(iii) Let Y3 = X. Find its cumulative distribution function and its density, in terms of Fx and fx

(iv) Assume now that X has standard normal distribution N(0,1): what is the density of X2?

Nov 13 2021| 07:57 AM |

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