3.1 Consider a random variable X with point probabilities P(X=k) =1/6 for k=1, 2, 3, 4,...

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3.1 Consider a random variable X with point probabilities P(X=k) =1/6 for k=1, 2, 3, 4, 5, 6. Draw the graph of X's distribution function F: R R. (5) 3.2 Consider a Random Variable Y with density function f(x) = 1 for x in the interval [0, 1]. Draw the graph of Y's distribution function F: R (5) R. 3.3 A red and black die are thrown. Let the random variable X be the sum of the dice, and let random variable Y be difference (red minus black). Determine the point of probabilities of X and Y. Are X and Y independent? (5) 3.4 A continuous random variable X has a density, F(x) = e-x [(for x greater than 0) and (for x less than 0)]. Determine the distribution function F. What is the P(x greater than 1)? (5) 3.1 Consider a random variable X with point probabilities P(X=k) =1/6 for k=1, 2, 3, 4, 5, 6. Draw the graph of X's distribution function F: R R. (5) 3.2 Consider a Random Variable Y with density function f(x) = 1 for x in the interval [0, 1]. Draw the graph of Y's distribution function F: R (5) R. 3.3 A red and black die are thrown. Let the random variable X be the sum of the dice, and let random variable Y be difference (red minus black). Determine the point of probabilities of X and Y. Are X and Y independent? (5) 3.4 A continuous random variable X has a density, F(x) = e-x [(for x greater than 0) and (for x less than 0)]. Determine the distribution function F. What is the P(x greater than 1)? (5)

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