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Random Variables : Continuous R.V., Exponenetial, R.V, Mean and Variance
Let X be a continuous random variable with probability density function f(s)= c(1 + s^2) for -2 <= s <= 2.a) Determine cb) Determine Pr {X <= 0}c) Determine the mean of Xd) Why is the previous answer fairly obvious?e) Determine the variance of Xf) Compute Pr {X = 2 | X = 0}g) Determine the cumulative distribution function
Let Y be an exponential random variable with parameter 1.5a) Compute Pr {Y=0}b) Compute Pr {Y > 2}c) Compute Pr {Y > 4 | Y > 2}d) Compute Pr {Y > 5 | Y > 3}e) Compute Pr {Y > 5.6 | Y > 3.6}f) Compute Pr {Y > x + 2 | Y > x } for x >= 0?g) What is E[Y]?h) What is the variance of Y
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