3) 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

4) 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