problem 1: The probability density function (pdf) of X is given by:
a) Verify that that f(x) is a legitimate pdf.
b) Sketch the graph of the pdf function.
c) Find the distribution function of X and sketch the graph.
d) Compute P(1< X < 2.3).
e) Find the expected value and the variance of X.
problem 2: Let the distribution function of X given by:
¦ 0 if x< -2
F(x) = 1/2 + (3/32)(4x -x^{3}/3) if -2 ≤ x < 2
¦ 1 if x ≥2
a) Graph the distribution function.
b) Compute P(X< 1).
c) Compute P(0.5< X <2.4).
d) Find the median.
e) Find the density function of X.