STAT-4033: Homework #4 Key
Section 2.3
Exercise 1
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.
Exercise 3
Notation: I will use the notation ij to denote the ith resistor havi
STAT-4033: Homework #3 Key
Section 2.1
Exercise 2
Part (a)
The sample space is S = cfw_1, 2, 3
Part (b)
P (Odd) = P (1 or 3) = 4/6 or .6667
Part (c)
This does not change the sample space. This is because the sample space is the set of possible outcomes.
W
STAT-4033: Homework #1 Key
Section 1.1
Exercise 1
Part (a)
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.
Part (b)
The populati
PROBABILITY I
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
Sasha Kocic
1
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
Section 4.1
Exercise 5
Part (a)
px = 0.5
Part (b)
py = 0.5
Part (c)
pz = P (X = 1, Y = 1)
= P (HH)
= 0.25
Part (d)
Yes. They are independent. Here, you can justify this by comparing probabilities and sample spaces. In this
scena