let x be a continuous rv with a probability density function pdf fx x cx2
Let X be a continuous RV with a probability density function (PDF)
fX(x) = cx2 for 0 < x < 3
= 0 otherwise
where c is a constant.
a) Find the constant c.
b) Find the probability that X takes on a value between 1 and 2 i.e., P(1 < X < 2) using the PDF.
c) What is the probability that X is equal to 1.5?
d) Find the CDF for the random variable X.
e) Use the CDF to calculate P(1 < X < 2).