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# HW5 - ECE 302 Homework#5 Due 2/18...

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ECE 302, Homework #5, Due 2/18 http://www.ece.purdue.edu/ chihw/ECE302 09S.html Question 1: [Basic] Write down the sample space and weight assignment (pmf) for a binomial random variable X with parameters n = 4, p = 1 / 4. Plot the pmf of X . Compute its mean E ( X ) and variance Var( X ). Question 2: [Basic] Write down the sample space and weight assignment (pmf) for a geometric random variable X with parameters p = 1 / 3. Compute its mean E ( X ) and the probability variance P ( X 5 and X is a prime number). Question 3: [Basic] Write down the sample space and weight assignment (pmf) for a Poisson random variable X with parameters α = 2. Compute its mean E ( X ) and the probability variance P ( X 5 and X is a prime number). Question 4: [Basic] This question demonstrates that we can easily convert one random experiment to a random variable. Carlos tosses two fair coins simultaneously and let Z denote the outcome. Namely, the possible outcomes of Z = ( Z 1 , Z 2 ) are S Z = { (0 , 0) , (0 , 1) , (1 , 0) , (1 , 1) } where Z 1 and Z 2 are the outcomes of the first and the second coins respectively.

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