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Problem 4 (9 points) a. (5 points) Let X be a discrete random variable with probability mass function p given by: a: -1 0 1 2 p(a): 1/4 1/8 1/8 1/2 and p(a) = 0 for all other a. a. Let the random variable Y be defined by Y = X^2, i.e., if X = 2, then Y = 4. Calculate the probability mass function of Y. b. Calculate the value of the distribution functions of X and Y in a = 1, a = 3/4, and a = ? ? 3. b. (4 points) Consider a random variable X that takes the values 0, 50, 100, 150, and 200, each with probability 0.2. Let Y = |X ? 100| be the (absolute) deviation of X from its average value 100. Specify the probability mass function (PMF) and cumulative distribution function (CDF) of Y completely. Explain.

          Problem 4 (9 points)
a. (5 points) Let X be a discrete random variable with probability mass function p given by:

a:    -1   0   1   2
p(a): 1/4  1/8 1/8 1/2

and p(a) = 0 for all other a.

a. Let the random variable Y be defined by Y = X^2, i.e., if X = 2, then Y = 4. Calculate the probability mass function of Y.

b. Calculate the value of the distribution functions of X and Y in a = 1, a = 3/4, and a = ? ? 3.

b. (4 points) Consider a random variable X that takes the values 0, 50, 100, 150, and 200, each with probability 0.2. Let Y = |X ? 100| be the (absolute) deviation of X from its average value 100. Specify the probability mass function (PMF) and cumulative distribution function (CDF) of Y completely. Explain.

Problem 4 (9 points)
a. (5 points) Let X be a discrete random variable with probability mass function p given by:

a: -1 0 1 2
p(a): 1/4 1/8 1/8 1/2

and p(a) = 0 for all other a.

a. Let the random variable Y be defined by Y = X^2, i.e., if X = 2, then Y = 4. Calculate the probability mass function of Y.

b. Calculate the value of the distribution functions of X and Y in a = 1, a = 3/4, and a = ? ? 3.

b. (4 points) Consider a random variable X that takes the values 0, 50, 100, 150, and 200, each with probability 0.2. Let Y = |X ? 100| be the (absolute) deviation of X from its average value 100. Specify the probability mass function (PMF) and cumulative distribution function (CDF) of Y completely. Explain.

Added by Amy G.

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