subset of population = sample (n)
SRS = each subset of population has chance of being selected
RS = each individual of population has chance of being selected
Data:
Qualitative - characteristics
nominal - no order, consists of names/labels (gender)
ordina
> load("/Users/aalbakri/Desktop/Stats HW1/Data.RData")
> #Data Set
> RunningSpeed<-c(1.25, 1.64, 1.91, 2.31, 2.37, 2.38, 2.84, 2.87,
2.93, 2.94, 2.98, 3.00, 3.09, 3.22, 3.41)
> #Building a histogram
> hist(RunningSpeed)
> #Finding the mean and standard de
stat224: Intro Stats for Engineers (003)
Table of Contents
Homework
05_Homework
05_Homework
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Relationship between Standard Normal and Normal RV
1.
2.
3.
1.
2.
4.
5.
6.
1.
2.
3.
If asked to compute normal probabilities:
convert X probabilities to Z probabilities
Use Table V (gives area from -infinite to z) for values of z
For Probabilities of the
Continuous Random Variable = RV that has an infinite number of
possible values that is not countable
example: length, depth, volume, time, weight
CRV described by probability density function (pdf) or probability
distribution of X, smooth curve
f(x) > 0 (
PMF: p(x) = P(X =x) = nCx*p^x*(1-p)^(n-x), x= 0 , 1 , 2 , n,
"put the individual back into the population" -> key phrase revealing
problem as Binomial
use PMF to describe the probability distribution of X by math formula
(slide 49)
Mean = = np
Variance =
Mean of DRV
= = [x*p(x)]
Variance of DRV
= x^2*p(x) - ^2 OR (x - )^2*p(x) (using chart slide 28) ->
standard deviation is square root of this
Interpretation of the Mean (Law of Large Numbers)
As the number of trials of the experiment increases, the mean
n
Chapter 6:
Random variable (RV)
is any function that assigns one (and only one) numerical
value to each sample point
Discrete RV -> countable (finite or infinite number of possible
values)
examples: # of sales, # of calls, # of people in line, # of
mistak
Box-and-Whiskers Plot
smallest data value that is larger than LIF (in usual range)
largest data value that is smaller than UIF (in usual range)
-essentially largest and smallest values within inner fences
-if median is closer to Q1 -> right skewed
-if med
If ? are independent events the P( limsup?) is either 0 or 1. It is of interest to determine when each of the cases occurs.
suppose P(An)<. Let B=cfw_: IAn()<. Show that P(B)=1.
n ?