Percentage points of the the standard normal, 1; and X2 distribution appear on the
Appendix 3 of the textbook.
Question 1
A _ n~3 _ a2 n _ 3 _
13(6) Ego/141)?) " E<2(mi7)2> X 02
d is an unbiased estimator of 6. (Note: 7é 1 =
COMMON DISTRIBUTIONS
Discrete
pmf
Mean
Binomial
p(y) =
0 < p < 1, n = 1, 2,
y = 0, 1, , n
Geometric
p(y) = p(1 p)y1
0<p<1
y = 1, 2,
Negative Binomial
p(y) =
0 < p < 1, r = 1, 2,
y = r, r + 1, r + 2,
Poisson
p(y) = e
y!
>0
y = 0, 1, 2,
n
y
py (1 p)ny
STAT 417 ASSIGNMENT 4
Read WMS Sections 9.1 to 9.3. Also read Section 7.3 on the Central Limit Theorem. Key
ideas are convergence in probability and the law of large numbers, denition of a consistent
estimator, convergence in distribution, the central lim
STAT 417 ASSIGNMENT 3
Read WMS Sections 8.3 to 8.6, 8.8, and 8.9.
1. Y1 , Y2 , . . . , Yn are a random sample from a normal distribution with unknown and .
We know that the quantity
(Yi Y )2
(n 1)S 2
=
2
2
has the chi-squared distribution with n 1 degrees
STAT 417 ASSIGNMENT 2
Read WMS Sections 7.1, 7.2, 8.1, and 8.2.
1. Suppose that Z1 and Z2 are independent standard normal N (0, 1) random variables.
What is the distribution of
Z1 + Z2
W =
2
2. Suppose that Z1 , Z2 , Z3 , and Z4 are independent standard
STAT 417 ASSIGNMENT 1
1. WMS Exercise 6.1.
Let Y be a random variable with probability density function given by f (y) = 2(1 y),
0 y 1, 0 otherwise.
a. Find the density function of U1 = 2Y 1.
b. Find the density function of U2 = 1 2Y .
c. Find the density
STAT 417 ASSIGNMENT 1
Read WMS Sections 6.1, 6.2, 6.3, 6.4(pages 310313 only), and 6.5. This reviews material
from STAT 416. In addition, review carefully the background for any techniques that seem
unfamiliar, particularly WMS Sections 3.1 to 3.3 and 4.1