630 Homework3 solution
2.4.2
(a). Since W is dened on interval [1, 4], thus P (W 5) = 0;
(b). P (W 2) =
4 2
4 1
2
= 3;
(c). P (W 2 9) = P (W 3) = 31 = 2 ;
1
4213
2 2) = P (W
2) = 41 =
(d). P (W
2 1
3.
2.4.4
In this question, we apply the fact that the i
STATISTICS 630 - Solution to Test I
June 21, 2011
1. Let A be the event that your right knee is sore on a given morning and B be the event
that your left knee is sore on that morning. Suppose that P (A) = 0.4 and P (B ) = 0.5.
What the probability that at
STATISTICS 630 - Solution to Test II
July 15, 2011
1. Suppose that the amount of a metal alloy produced by a factory each week is uniformly
distributed between 40 kilograms and 64 kilograms, and that the amounts produced
each week are independent. Use the
630 homework7 solution
Editor:
4.6.1
(a). Since X1 and X2 have the normal distributions and they are independent, thus
U and V are also normal random variables. Since E [U ] = 3 + 40 = 43, V ar(U ) =
V ar(X1 ) + 52 V ar(X2 ) = 629 and E [V ] = 18 + C (8)
STATISTICS 630 - Solution to Test I
October 8, 2010
1. Suppose that we toss four fair coins.
(a) Find the probability of tossing exactly one head.
Let X = the number of heads. Then P (X = 1) =
4
1
0.54 = 1/4.
(b) Find the probability of tossing an odd num
Statistics 630
1 The Likelihood Function
In the previous chapter, we introduced statistical models cfw_P
: which
describe the probability models that could generate the observed data. In this
chapter we will develop inferences that depend only on the mod
Statistics 630
1 Introduction
In the later chapters when we study the application of probability theory to
statistical inference, we will often consider a random sample of size n from a
given distribution.
We say that X1 , . . . , Xn is a random sample fr
STAT 630 Formulas for Test 1
Axioms of Probability
(i) P (A) 0 for any event A;
(ii) P (S) = 1; (
)
(iii) For mutually exclusive events A1 , A2 , . . ., P
Ai = i=1 P (Ai ).
i=1
Probability of a Union: P (A B) = P (A) + P (B) P (A B).
Permutations: Pk,n =
Statistics 630
1 Probability Models
In the first four chapters we covered probability theory and learned how to carry
out calculations based upon knowing the underlying probability model.
Example 42
Goals Scored in a Soccer Match
Let X
= the number of goa
Statistics 630
1 The Bayesian Approach to Parameter Estimation
In the Bayesian approach, we suppose that the unknown parameter is a random
variable with a prior distribution (). For a given value of , the data S have a
pdf or pmf f (s). The joint distribu
Statistics 630
1 Random Variables and Distributions
Random variables are the main link between probability and statistics. In statistics
we observe numbers (or data) as the result of an experiment, and a random
variable links the numbers to the probabilit
Performing Hypothesis Testing for One-sample t-tests in Excel 2016
You should already have the Excel tutorial file open.
1. Copy a single continuous variable into a new sheet. In this case we will copy Phone
Time.
2. Create a table as the one on the right
Statistics 630 - Assignment 3
(due Wednesday, September 21, 2016, 11:59 pm)
Instructions:
The textbook exercises are in the book by Evans and Rosenthal. This assignment
covers material from Chapters 2 discussed in Lectures 0709.
Whether you write out th