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here is a first example of using the transformation technique let the random variable X be uniformly distributed between 0 1 find the cumulative distribution function of the random variable Y which is the square root of X now in this picture down below here I have X on the horizontal axis I have the random variable Y on the vertical axis if X lies between 0 1 then Y which is the square root of x will also lie on 0 1 but notice as I took a couple points here at point two point four point six and point eight and I transform them using Y is equal to the square root of x as my transformation more of the points towards the top here they kind of get bunched up more towards the higher part of the distribution of Y and thats something that were going to see as we work through the details on this transformation go ahead and start out here with FX of X notice Ive got to put in that capital X here as a subscript because its not clear whether Im dealing with X or Im dealing with Y so I
