STAT-4033: Homework #4 Key
We need P (A B) = P (A) P (B) for the independence to be true. If P (A B) = 0.2 and P (A) = 0.8, then
P (B) = 0.2
0.8 = 0.25.
Notation: I will use the notation ij to denote the ith resistor havi
STAT-4033: Homework #3 Key
The sample space is S = cfw_1, 2, 3
P (Odd) = P (1 or 3) = 4/6 or .6667
This does not change the sample space. This is because the sample space is the set of possible outcomes.
STAT-4033: Homework #1 Key
The population is all potential times the chemical process could be run in the future, or it is all potential
yields of the chemical process. This is a conceptual population.
Test 2 - review topics
August 5, 2008
1. Random variables
(a) Random variables - real valued functions X on the sample space S , i.e. X : S R.
Cumulative distribution function is dened as:
F (x) = P cfw_X x,
< x < .
2. Discrete random varia
Some continuous and discrete distributions
Table of contents
I. Continuous distributions and transformation rules.
A. Standard uniform distribution U [0, 1].
B. Uniform distribution U [a, b].
C. Standard normal distribution N (0, 1).
D. Normal distributio
M 362 Probability Lecture Notes
August 11-15, 2008
6.3 Sums of independent random variables
X and Y are independent continuous random variables with probability density functions
fX and fY .
FX +Y (a) = P cfw_X + Y < a =
fX (x)fY (y ) dx dy
STAT-4033: Homework #8 Key
px = 0.5
py = 0.5
pz = P (X = 1, Y = 1)
= P (HH)
Yes. They are independent. Here, you can justify this by comparing probabilities and sample spaces. In this