# 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

Let X be a continuous RV with a probability density function (PDF)

f_{X}(*x*) = c*x*^{2} 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).

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