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?