Stat 273
Tutorial 1
Solutions
1) Name some useful features in the Data Analysis Toolpack.
Descriptive Statistics and Random Number Generation
2) Name some useful functions from the fx (Paste function) window.
Math and Trig COMBIN, TRUNC, EXP, FACT, ABS, I
Stat273
Tutorial 7
The first question (Q.1) is given with full solution here. Go through it, and use it as
a guide to answer Q.2 and Q.3, which are similar.
In this tutorial we
Use both Excel and Wolfram Alpha (WA) to find solutions to continuous
distrib
Stat273 Introduction to Probability
Tutorial 9
Solution
Generating probability Distributions in Excel
1. (discrete)
X values: Obtain all values in the range of x
p(x):
Obtain corresponding probabilities
Graph, using points
F(x):
Either
1. sum previous pro
Stat273
Tutorial 6
In this tutorial we
introduce you to some useful features in Wolfram Alpha
(www.wolframalpha.com).
use the integration to help solve probability problems for
continuous random variables.
graph theoretical probabilities
We shall revie
Stat 273
Solutions to Tutorial 12
Question 1
fx 1 , x 2 x 1 x 2
(This 3-D joint pdf graph is for your reference only.)
1/2
1
1
0 1/4 x 1 x 2 dx 2 dx 1
(a) PX 1 0. 5, X 2 0. 25
1/2
1/4 0 x 1 x 2 dx 1 dx 2
Alternatively,
1
(b) f 1 x 1 0 x 1 x 2 dx 2 x 1
Stat273
Tutorial 10
In this tutorial we
r Use Excel to obtain probabilities of the 2 and F distributions.
rUse Excel to assist in carrying out an F-test for equality of variance.
rUse WA for integration.
We shall review the following concepts from Lecture
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Stat273 Introduction to Probability
Tutorial 7
Solution
1. Find the integral of the function and evaluate the
integral between the given limits, i.e. both definite
and indefinite integrals.
f(x) = 2x
0<x<1
2 xdx = x
2
1
e
0
0<x<1
2
dx =
f(x) = x2
0<x<1
1
Stat273
Tutorial due in week 13
In this tutorial we use Wolfram Alpha (WA) to investigate homogenous
Markov Chains
We find and interpret
r Stationary distribution
r A Markov Chain with absorbing states
Matrices in WA
Please give a look at: http:/www.wolfr
Stat273
Tutorial due in week 12
In this tutorial we
r Use Wolfram Alpha (WA) to find Probabilities of continuous joint
probability functions.
We shall review the following concepts from Lectures.
q Joint Distributions
q Marginal distributions
q Conditiona
STAT 273 Risk and Chance
Tutorial 13 Solutions
(sorry for some problems in displaying symbols)
Question 1
(a)
p11 = p11 = p11 = p11
= P(move from machine i to i)
= P(move from machine i to i | won in machine i) P(won) +
P(move from machine i to i | lost i
Stat273 Introduction to Probability
Tutorial 9
In this tutorial we
Use the idea that random numbers from U[0,1] can be considered as
random numbers from a cdf.
Use Excel to generate random numbers from an Exponential
distribution.
We shall review the fo
Stat273
Tutorial 8
In this tutorial we
Use both Excel and Wolfram Alpha (WA) to explore gamma and beta
distributions, including generating graphs and solving probability
problems.
Sum of random variables from distributions
Chi-squared goodness of fit t
Stat 273
Tutorial 4
In this tutorial we
Review discrete variable probability distributions
practice calculating expected values and variances using Excel.
graph theoretical probabilities
graph frequencies obtained from simulation.
We shall review the
Stat 273 Introduction to Probability
Solution Tutorial 4
1. What is the random variable in this situation?
X = Payout from KG-bird
2.
X is discrete. It can only assume a certain
number of values.
3. What are the values of the random variable?
X = 0,2,5,10
Stat273
Tutorial due in Week 3
From lecture 1
Some Counting Exercises
q If a set A has m elements, and a set B has n elements then it is possible to
form mn pairs, containing one element from each set.
q An ordered arrangement of r distinct objects is cal
Stat 273: Introduction to Probability
Tutorial due in week 3
Solutions
From Lecture 1
1. How many different hands of poker (5 cards) are possible from a 52 pack of
cards.
Number of different hands=52C5= 52*51*50*49*48/5!
= 2,598,960
2. How many different
Stat273
Tutorial 5
Aim:
To become familiar some discrete probability distribution, namely
Binomial Distribution
Negative Binomial Distribution
Hypergeometric Distribution
We use the BINOMDIST, NEGBINOMDIST and HYPGEOMDIST statistical
functions in EXCEL to
Stat273
Tutorial 4
Aim:
To become familiar some discrete probability distribution, namely
Binomial Distribution
Geometric Distribution
Poisson Distribution
We use the BINOMDIST, NEGBINOMDIST and POISSON statistical functions in
EXCEL to assist in calculat
Stat273 Introduction to Probability
Tutorial 6
Solution
1. For each of the following
write down the probability function
provide a table showing the probability distribution and cdf,
provide a display of the probability distribution
and calculate
a) P
Stat273
Tutorial 1
In this tutorial we shall cover the following:
q Installing the Data Analysis Toolpak in Excel (We will be using the
Random number generator from the Toolpak.)
q Hot Keys in Excel
q Insert Function Tool in Excel
We shall review the foll
Stat273
Solution
Tutorial 11
Aims:
Use Excel to obtain probabilities of the 2 and F distributions.
Use Excel to assist in carrying out an F-test for equality of variance.
Simulation study to demonstrate the distribution of sample variances.
Use WA for