Continuous r.v., exponenetial, r.v, mean and variance

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Reference no: EM13122428

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 c
b) Determine Pr {X <= 0}
c) Determine the mean of X
d) Why is the previous answer fairly obvious?
e) Determine the variance of X
f) Compute Pr {X = 2 | X = 0}
g) Determine the cumulative distribution function

Let Y be an exponential random variable with parameter 1.5
a) 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

Reference no: EM13122428

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