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Quiz 3

# Quiz 3 - X is F X x = x< 0 x/4 ≤ x ≤ 4 1 x> 4...

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University of Arkansas at little Rock Department of Systems Engineering SYEN 3314 Probability and Random Signals Summer 2009 Quiz 2 Wednesday, June 24, 2009 This is a closed book Quiz. Calculators are not allowed. The quiz has 3 questions to be answered in 15 mn Please be neat, we cannot grade what we cannot decipher. Name 1

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Question 1 Let X be a noise voltage that is uniformly distributed in S X = {- 3 , - 1 , +1 , +3 } with p X ( k ) = 1 4 for k S X . Let Z = X 2 . Find 1. PMF of Z , P Z ( z ) 2. E[Z] 2
Question 2 The cumulative distribution function of the random variable

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Unformatted text preview: X is F X ( x ) = , x < 0; x/4 , ≤ x ≤ 4; 1 , x > 4. Calculate the following probabilities 1. P [ Y ≤ 1] 2. P [2 < Y ≤ 3] 3. P [ Y ≤ 1] 4. P [ Y > 1 . 5] 3 Question 3 Random variable X has probability density function f X ( x ) = b cxe-x/ 2 , x ≥ 0; , otherwise. Find the following 1. the constant c 2. P [0 ≤ X ≤ 4] 3. The CDF F X ( x ) 4. P [-2 ≤ X ≤ 2] 4...
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• Spring '08
• Ferry
• Probability distribution, Probability theory, probability density function, Cumulative distribution function, Department of Systems Engineering

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Quiz 3 - X is F X x = x< 0 x/4 ≤ x ≤ 4 1 x> 4...

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