The document discusses properties of a continuous random variable x with a specified density function, including the requirement to show that the area under the curve equals 1. It also outlines the calculations needed for specific probabilities, expected value, variance, and standard deviation for both x and a transformed variable (3x + 1). Key problems include finding probabilities for given ranges and the statistical measures e(x), v(x), and their transformations.

1. A continuous random variable X has a density function given by
Show that the area under the curve is equal to 1.
Find P(2 < X < 2.5).
Find P(X < 1.6)
Find P(x< 1)
Find P(x > 2)
E(X), V(X), and E(X).
E(3X +1), Var(3X + 1), and SD(3X + 1)
Q7: A continuous random variable X has a density function given by f(x)={210,1x3otherwise i)
Show that the area under the curve is equal to 1 . ii) Find P(22) vi) E(X),V(X), and E(X). vii)
E(3X+1),Var(3X+1), and SD(3X+1)