Cf.
Standard normal
distribution
1
Note on skewness
1) Skewness characterizes the degree of asymmetry of a distribution around its mean.
2) Positive skewness indicates a distribution with an asymmetric tail extending towards
more positive values (right sk
Describing Data with Pictures
There are several ways to describe data. One of way is to use pictures. These techniques
include frequency distributions, histograms and bar graphs. We will focus on histograms
and bar graphs.
Histograms
What are they?
A hist
Chapter 2: Probability
2.1: Sample space
Experiment - an activity for which an outcome is
uncertain
Example: Flip a coin head or tail are
unknown until it is observed
Example: Roll a pair of dice the numbers
rolled are unknown until they are observed.
Exa
Descriptive Statistics: Describing Data with Numbers PART 2
Measures of Variability
Variability refers to how dispersed are the data points in a distribution, and how similar or
different each data point is from the other data points.
There are three comm
Ch. 3 - Probability
Random Phenomenon: a situation where we know the possible outcomes ahead of time,
but individual outcomes are only known after the situation occurs.
e.g. Roll a die, toss a coin, whether it will rain tomorrow, whether an item/unit meet
Ch. 5 - The Normal Distribution
1
Definition and Properties
Normal Distribution: If a continuous random variable X follows a normal distribution
with mean and standard deviation , we write
X N (, 2 )
The normal distribution has a continuous density summar
Ch. 7 - Normal Probability Approximations
1
Central Limit Theorem
Population vs. sample, parameter vs. statistic
Population: contains the entire collection of individuals we want to study
Sample: subset of individuals selected from the population
Paramete
Ch. 8 - Statistical Modelling and Inference
Statistical Inference: the process of inferring something about the population based on
what is measured in the sample.
We will learn:
1. Point Estimation - estimate an unknown parameter using a single number ca
Ch. 1 - Summary and Display of Univariate Data
Statistics is a science involving the design of studies, data collection, summarizing data,
interpreting resulting and drawing conclusions.
Often in statistics, we want to know something about a certain popul
Ch. 6 - Some Probability Models
First recall some concepts from Ch. 4.
Discrete Random Variables:
For discrete random variables, we have probability mass functions (pmf) (denoted f (x),
which gives the probability for each possible value x of X. Recall, f
Study guide questions on random selection
1. The following marks are the test 1 marks for 10 randomly selected STA100 students:
67, 34, 98, 78, 76, 55, 80, 49, 91, 66. What is the coefficient of variation for this sample?
*a. 0.28
b. 0.30
c. 0.38
d. 0.25
Study guide questions on variance
1. Given a negatively skewed distribution with a median of 8 and a mode of 10. Which of
the following is not a possible value for the mean?
a. 7
b. 1
*c. 12
d. 5
e. 3
2. Which of the following data sets has the largest va
Study questions on quartile
1. You are given the following data set: 15, 12, 11, 13, 10, 23, 19, 18, 11, 8. Find the
values of the lower quartile, median, upper quartile and inter-quartile range respectively.
a. (11, 12.5, 16, 5)
b. (11, 13, 17, 6)
c. (11
Ch. 11 - Simple Linear Regression
Objective: to describe a linear relationship between two quantitative variables using a model.
The model fits a straight line to the data and can be used to make predictions on the
response variable (y) given the explanat
Yuyin Chen
Assignment Assignment-03 due 10/05/2016 at 09:00pm PDT
STAT241-251-101 2016W1
Mean: We list out all 8 possible outcomes with their probabilities as shown below.
1. (7 points) The continuous random variable X has a probability density function (
Yuyin Chen
Assignment Assignment-01 due 09/18/2016 at 09:00pm PDT
STAT241-251-101 2016W1
(b) The number of students with under 10 dollars in their
possession is closest to
1. (2 points) Consider the histogram shown below.
A. 40
B. 50
C. 60
D. 70
(c) T
Yuyin Chen
Assignment Assignment-09 due 11/30/2016 at 09:00pm PST
1. (10 points)
A dairy farmer is looking at methods for transporting milk
from her farm to a dairy plant. Three different methods are
trialed over fourteen working days, and the daily costs
Yuyin Chen
Assignment Assignment-05 due 10/23/2016 at 09:00pm PDT
4. (1 point) A random variable X is normally distributed,
with a mean of 27 and a standard deviation of 2.4.
Which of the following is the appropriate interquartile range
for this distribut
Yuyin Chen
Assignment Assignment-07 due 11/06/2016 at 09:00pm PST
STAT241-251-101 2016W1
0.87.
1. (4 points) The wait time (after a scheduled arrival time)
in minutes for a train to arrive is Uniformly distributed over the
interval [0, 15]. You observe t
Yuyin Chen
Assignment Assignment-06 due 11/06/2016 at 09:00pm PST
Part c) We have X Geometric(p = 0.2397), and we wish
to compute P(X is odd). This is
1. (3 points) The life times, Y in years of a certain brand of
low-grade lightbulbs follow an exponentia
Yuyin Chen
Assignment Assignment-04 due 10/09/2016 at 09:00pm PDT
D
1. (1 point)
The time T required to repair a machine is an exponentially
distributed random variable with mean 5.5 (hours). What is the
probability that a repair takes at least 12 12 hou
Yuyin Chen
Assignment Assignment-08 due 11/23/2016 at 09:00pm PST
We wish for the width = 2 1.96 p50n < 26
1. (1 point) In a study to estimate the proportion of residents
in a city that support the construction of a new bypass road in
the vicinity, a rand
Yuyin Chen
Assignment Assignment-02 due 09/25/2016 at 09:00pm PDT
STAT241-251-101 2016W1
different results), find the following (giving answers to two decimal places):
Part a) The sample mean is
(sec).
Part b) The sample variance is
(sec2 ).
Part c) The s
Study questions on outliers
1. You are given the following data set: 2 5 9 13 27. Which of the following statements
is true?
a. There are no outliers
*b. Only 27 is an outlier
c. 2 and 27 are outliers
d. 13 and 27 are outliers
e. None of the above are tru
Ch. 4 - Random Variables and Distributions
Random variable: a function (rule) that assigns a number with each outcome in the
sample space. Usually denoted with capital letters, (X, Y, Z) and its possible realized values
are denoted by the same lowercase l