M 362K, Spring 03, Smith

## Assignment for Wednesday, November 12

I. Read Section 6.2: Independent Random Variables
• Be sure to learn both the technical definition of independent random variables and the intuitive idea that the definition is making precise.
II. Do the following practice problems to build your understanding:

1. For each of the following joint probability mass functions, decide whether the (discrete) random variables X and Y are independent. Explain why.

a.                 (1/25)(x2+y2)     if x = 1,2, y = 0, 1, 2
p(x,y) =
0                otherwise

b.                 (1/7) x2y        if (x,y) = (1,1), (1,2) (2,1)
p(x,y) =
0            otherwise

2. p. 292 #20

3. X and Y are independent discrete random variables each having the probability function

p(x) = (1/2)(2/3)x,    x = 1, 2, 3, ...

Find P{X = 1, Y = 2} and P{X + Y = 3}

4. From an ordinary deck of 52 cards, six cards are drawn at random and without replacement. Let X be the number of hearts, Y the number of diamonds. Are X and Y independent?