Chapter 1'2.
5;hp\e [\ihear regcesswl.
Let (xwY), H.) (gman beauv.5. 0+ observakmng
DaferwaMbhl relatonsklp v Y: {(x)
Nondetummushc or probab'ilnsl'lk relahonslmfp
E25 Let X: height rwezgort. Lef(¥:.,1,-~, ()g , m
be 04.5 of taught: and wetghts measured
o
Class examples (Sect. 4.1)
1. The number of interviews that a student has prior to getting a job is represented by the random variable X with
36
probability function () = 49 2, for x = 1,2,3. Find the expected number of interviews prior to getting a job.
Class examples (Sect. 3.1-3.2)
1. Specify if the random variables representing the following are discrete or continuous:
(a) The lifetime of a device:
(b) Number of students in a random class:
(c) Number of trains arriving to a station:
(d) Time until the
Binomial and Multinomial Distributions
October 20, 2016
Bernoulli Trials
An experiment with only two possible outcomes, typically denoted success and failure.
If P (success)=p, then the P (f ailure) is 1 p (sometimes denoted q).
Note that success does not
Class examples Counting sample points (Sect. 2.3)
1. An employee from Washington state can choose among three group life insurance plans and five group health
insurance plans. If the employee chooses one life insurance plan and one health insurance plan,
Class examples Conditional probability, independence, and the product rule (Sect. 2.6)
1. In a city, 60% of all households get Internet, 80% get cable, and 50% get both services. If a household gets at
least one of these services:
(a) what is the probabil
Class examples (Sect. 3.3)
1. Let T represent the time until failure (in years) of a randomly selected component. We believe that T has density
function f (t) = 0.5 e0.5t, t 0.
(a) Verify that f (t) is indeed a density function.
(b) What is the cumulative
WASHINGTON STATE
g: UNIVERSITY
/ VANCOUVER
Probability and Statistics
STAT 360, Fall 2016
Class examples Introduction to Statistics and Data Analysis
1. The following is data associated with a study conducted at Virginia Polytechnic Institute and State
g .10.
6'
e.-
7/2gz than 1:7 Swot/MA 3&0
Ho: p = 40 v. H.: p 96 40, where p is the true average bum-out amperage for this type of fuse. The
alternative reects the fact that a departure from p = 40 in.either direction is of concern. A type I error
w
2.
a. The sample mean is the center of the interval, so 2: =115 .
b'. The interv'al 114.4, 115.6 has th 0 I '
Wider intmag. ) e 9041 condence level. The h1gher condence level w111 produce a
7 \k 4.
96(3) $58.3i1.18=(57.1,59.5).
1.
. 58.3i-
a J25
b. 58
(kaptzr 7 notes
Condence; Inter vols (Lil's !
m n) "')xn a
where r Is Known , u {IS unknown _ :3: 7-L loo"
EL. Lat P: StUCLthS} ,
0% cu student sded'ed. at random. and
assume. X~N(u,¢r"l. Let XU«-»,xwe be a r.$.
setected selected {ram X amok Sup 9054.
1
Ck apter- 3 Note:
Rand om vanable (y) 1- For (3 anoL-SIC} riv. 13
«no! rule. that assacm 11$ (1 number wntin each
outcome 465)|.¢.,og av. !S a. function from >
5(domain] to a; subset of the real 1m; (range!
E; E: 0'0 1 fag-r: dale-a (redqrcanl
S : 30:4) 1
Ckapfer 9- leciure note; q'l
Compartrlcj two population mean 5
Lat Xumm [09- a r25. from X when E(x),M,va,(,¢Lq1
LU: Yum)? baa as. from Yuhere E($j),M1!var(y),.-:
Want to estlmate Jug-ML,
use X to esfmuteu, Jase Y to eshmafe ML =3
usua' 5tl1;1at0r for Mf
\/ 1hr Mafk/Sbg36
Chaptu'Z-vhdfu _
Exp- (mg process {Luff generqfes data,
Dife'rm'm'téfm ups. and model-S '
Probabltit'q '
Random exp v E Sat}$FleS . '
' V as Can be. repeated'lhdemteg under {he
same COQJHIOILS'
a 3 5H! pass: lz_oafcomes are ITnown an
'
Chapter 6 11an: 5"
Eshhatfom
Let X.,-~.,X, be a random sample. taken from HR
st. of X and let x ,1 denote the observed Sang-lg
Let 6 Jennie Some unknown parameter
ng. Am, sfaikc é/«S (3g,ng used it; esflvhafe
e is Camden estrufar of e. The specnic Value.
ChApier 5 notes 5. I
Tut'an d?str.\outqd r.v.5
Q51}, Lat X'. Sari! 9nd, L(IS-i «Y be r.v.5.
Then (187)154ny a: a. Z-alu'n'ensmnal nu
Nets, La£_ILX,Y].S~Rx.r be. a. Ldum (nu. I?
XanA l are both ohscrete , (Xl) ls drscxd;
IFXanAi are. hath (amt.l (X)?! 15 c
Chapter L! hofES A
C I .
Q35? A nv. X: S* Rx \5 cptleot a. continuous
r,v. IF Rx contmfns cm Interval or some
union 0* antermisofuaiues an the real hue.
[M Lei Xbe. 0. (out. nu. Tim probabthfty calamity
n. (pm?) of X,denoted by {x64 or {/36}, {:5 q.
fn. w
Class examples Probability of events, and additive rules (Sect. 2.4-2.5)
1. The probabilities that a car mechanic will service 3, 4, 5, 6, 7, or 8 or more cars on any given workday are 0.12,
0.19, 0.28, 0.24, 0.10 and 0.07, respectively. What is the proba