hw12 - If g ( ) is replaced by h ( x ) = p | x | determine...

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ENEE 324 ASSIGNMENT 12 Due Tue 10/20 Problem 12A Consider the transformation (function) g ( x ) = 0 , x < 0 x, x 0 (i) (2 pts.) If X is a continuous random variable with range S X = R , what is the range S Y of Y = g ( X )? Is the distribution of Y continuous, discrete, or of mixed type? (ii) (3 pts.) Let X be a continuous random variable having arbitrary range. For every y R , give an expression for the cdf F Y ( y ) in terms of the cdf F X ( · ). (iii) (10 pts.) Using the result of part (ii) above, determine the cdf F Y ( y ) and the pdf f Y ( y ) in each of the following cases: X is uniform over [ - 1 , 4] X is exponential with parameter λ = 2 (iv) (5 pts.)
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Unformatted text preview: If g ( ) is replaced by h ( x ) = p | x | determine the cdf and pdf of Y = h ( X ) when X is Gaussian with mean 1 and variance 4. Problem 12B The pdf of the random variable X is shown below. f X ( x ) 0 4 6 x 1/3 1/3 (i) (5 pts.) Determine E [ X ]. (ii) (5 pts.) Determine E [ X 2 ]. (iii) (5 pts.) Determine E [ Y ], where Y = min { X 2 , 4 } . (iv) (5 pts.) For the random variable V with pdf as shown below, determine the position a of the discrete mass so that E [ V ] = E [ X ]. f V ( v ) 0 a 4 8 v 2/3 1/12...
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