Stat 251 Midterm 2 Version A Solutions
Let X be Annes arrival time and Y be Claires arrival time measured in minutes after 12:00
We want to find the probability that Anne arrives before Claire:
P (X < Y )
Assignment Assignment-02 due 09/25/2016 at 09:00pm PDT
different results), find the following (giving answers to two decimal places):
Part a) The sample mean is
Part b) The sample variance is
Part c) The s
Statistics 241/251: Lab 3 Pre-reading
Learn to use R to
Obtain probability mass functions f (x)
Obtain cumulative distribution functions F (x)
Simulate random draws
Visualize probabilities using R (optional)
Stascs 241/251: Lab 2 Pre-reading
Understand your responsibilies during the lab
Learn how to read a data le into R
Random variables (Discrete)
Expected value of a random variable
Variance of a random variable
1. Your Responsibilies
Statistics 241/251: Lab 3 Exercises Distribution Functions
The Teaching Assistants in the STAT 241/251 lab noticed that the students raised questions at a rate of 2 questions
per minute, and the time between questions were Exponentially distributed.
Statistics 241/251: Lab 2 Exercises - Probability and Random Variables
Important: You will submit only one solution per group. However, each member should participate in
completing the exercises. Keep track of time so that you will finish on time.
Statistics 241/251: Lab 5 Solution
Please write down your answers neatly and do show your work (including R code).
Please use proper notations in your solutions.
1. Calculate th
Compliment of A? C
Are A and B Disjoint? Yes
Are A and C Disjoint? Yes
Are B and C Disjoint? No
Are complimentary events always Disjoint? Yes
Are Disjoint events always complimentary? No
General form: Let A1 , A2 , ., An be disjoint events that together f
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 populat
STAT 241/251 Assignment
Winter 2016/17 Term 1
Please attach a cover sheet (posted on Connect) when you hand in the assignment.
Due: Nov 25 at 4pm in the STAT241/251 dropbox in ESB
Total marks: 30 marks
Instructions: Typewritten answers are preferred. If y
Please attach a cover sheet and staple your assignment
Due: 6pm on Thursday, June 1, 2017 in STAT 241/251 dropbox in ESB
Total Marks: 30
Make sure you show all your
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
Study questions on outliers
1. You are given the following data set: 2 5 9 13 27. Which of the following statements
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. 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
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. 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. 7 - Normal Probability Approximations
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
Ch. 5 - The Normal Distribution
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. 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
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
Chapter 2: Probability
2.1: Sample space
Experiment - an activity for which an outcome is
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.
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.
What are they?
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
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?