STAT 270 Lecture 16: 4.1 Random Variables

Consider two independent random variables X1 ∼ U(0, 7), X2 ∼ U(0, 1). For the random variables Y = X1 + X2:

• What is the support of the distribution? Is the distribution continuous, discrete or mixed?

• Draw the probability distribution function of the random variable? Justify your answer with either theoretically or logically.

Suppose X and Y are random variables with joint density function.

(a) Verify that f is indeed a joint density function