. Use R to plot the probability density (3.7) of an exponential random variable for values of λ = 0.5, 1.0, 5.0.   . For the exponential distribution (3.7) calculate the mean and variance. [Hint: Use...

.
Use R to plot the probability density (3.7) of an exponential

random variable for values of λ = 0.5, 1.0, 5.0.

.
For the exponential distribution (3.7) calculate the mean and

variance. [Hint: Use integration by parts.]

.
For a distribution with probability density function f(x) = 3

8x2

for 0 ≤ x ≤ 2 and f(x) = 0 elsewhere, find P(0 ≤ X ≤ 1), EX, EX2, and

VarX.