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A box contains four balls, numbered 1 through 4. One ball
Chapter 5, Problem 160SE(choose chapter or problem)
Problem 160SE
A box contains four balls, numbered 1 through 4. One ball is selected at random from this box. Let
X 1 = 1 if ball 1 or ball 2 is drawn,
X 2 = 1 if ball 1 or ball 3 is drawn,
X 3 = 1 if ball 1 or ball 4 is drawn.
The Xi values are zero otherwise. Show that any two of the random variables X1, X2, and X3 are independent but that the three together are not.
Questions & Answers
QUESTION:
Problem 160SE
A box contains four balls, numbered 1 through 4. One ball is selected at random from this box. Let
X 1 = 1 if ball 1 or ball 2 is drawn,
X 2 = 1 if ball 1 or ball 3 is drawn,
X 3 = 1 if ball 1 or ball 4 is drawn.
The Xi values are zero otherwise. Show that any two of the random variables X1, X2, and X3 are independent but that the three together are not.
ANSWER:
Solution:
Step 1 of 2:
Given that, a box contains 4 balls, numbered 1 through 4. One ball is selected at random from this box.
Let
1, if ball one or ball two is drawn
if ball 1 or ball 3 is drawn
if ball 1 or ball 4 is drawn
Here we have to show that any two of the random variables are independent but that the three together or not.