EE351KHW_14Fall2007

# EE351KHW_14Fall2007 - y over which it is valid(b Y E(c Y...

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THE UNIVERSITY OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering EE 351K • Probability and Random Processes • Fall 2007 Assignment No. 14 Do these problems, but do not turn in. All students will receive credit (30/30) for this assignment. Please include the following information on the first page of each assignment: (1) Your name (printed legibly), (2) Course number EE 351K , (3) Assignment Number , and (4) Due Date . Thank you. Problem 1 Consider the following exponential distribution. otherwise x e x f x X 0 0 3 ) ( 3 = If 3 2 + = X Y , find (a) The pdf of Y , and indicate the range of
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Unformatted text preview: y over which it is valid. (b) ] [ Y E (c) ] [ Y V (d) Y σ Problem 2 Consider the following normal distribution ∞ < < ∞ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − = x x x f X , 8 ) 10 ( exp 2 2 1 ) ( 2 π If 20 4 + = X Y , find (a) The pdf of Y , and indicate the range of y over which it is valid. (b) ] [ Y E (c) ] [ Y V (d) Y Problem 3 Consider the following pdf otherwise x x x f X 1 2 ) ( ≤ ≤ ⎩ ⎨ ⎧ = Determine the pdf of Y , where 2 X Y = . Indicate the range of y over which the pdf of y is valid....
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