Statistics 210 FC
Assignment 1
Due: 3PM, March 27th , 2015
1 Jenny is planning to go tramping next Sunday. The weather forecast
(for the next Sunday) indicates that there is a 40% chance of rain,
a 50% chance of wind and a 30% chance that there will be ra
STATS 210
Tutorial 6
1. President James Abram Gareld (1831-1881)
was an American president with lots of children.
He had 5 sons and 2 daughters. He also gave his
name to the cartoon character Gareld, although
the resemblence is not entirely convincing.
Su
STATS 210
Tutorial 4
1. For each of the following descriptions, say whether the random variable X is or is not a
Binomial random variable. If X is Binomial, give the values of the parameters n and p.
If X is not Binomial, give a brief (few words) reason w
STATS 210
Tutorial 3
1. Toms house is on the bus route for the
Link Bus service in central Auckland.
All Link Buses are coloured a distinctive
green colour.1 However, there are also other
bus services that are green. Tom has been
recording his observation
STATS 210
Tutorial 5
1. John Key and David Shearer are running for President of the Matchstick Corp. As usual,
their election campaign turns into a bitter ght. Their biggest argument is about the
statistical properties of the opinion polls. John Keys camp
STATS 210
Tutorial 2
The inhabitants of Planet Zog come in three dierent colours: red, orange, and green.
(This diversity can be very useful: for example, dierent coloured Zoglins can be employed
three at a time as trac lights.) In the whole population, 4
STATS 210
Tutorial 5
Model Answers
1.(a) Let X be the number of Shearer-voters out of 1000 respondents.
X Binomial(1000, pS )
H0
H1
:
:
pS = 0.4.
pS = 0.4.
(two-sided test)
(3)
(b, c) Under H0 , X Binomial(1000, 0.4).
The probability function of X peaks a
STATS 210
Tutorial 1
Tom has a complicated social life involving lots of girlfriends, although for some reason
he has no other friends. He gets three dierent types of phone calls: all his calls are either
wrong numbers, girlfriends, or somebody trying to
STATS 210
Tutorial 0
Free variables and dummy variables.
Look at the expression below:
10
ax2
x=1
There is an important dierence between the variables x and a in this expression:
a is a free variable. This means:
(i) The expression would still make sense
STATS 210
Tutorial 4
Model Answers
1.(a) Yes: X Binomial(n = 500, p = 0.14).
(b) Yes: X Binomial(n = 8, p = 0.7).
(c) No: not a xed number of trials (attempts until the rst success).
(d) Yes: X Binomial(n = 12, p = 0.02).
(e) No: not a xed number of trial
STATS 210
Tutorial 2
Model Answers
(a) Yes, events R, O, and G do form a partition of the sample space.
There is no overlap between the events, because a Zoglin cannot be two dierent
colours at once.
The events collectively cover all possible outcomes i
STATS 210
Tutorial 0
Model Answers
n
n
k2.
2
pk = p
1.(a)
TRUE. k is dummy. p and n are free.
k=1
k=1
n
n
n2 . FALSE. k is dummy. n is free.
2
kn = k
(b)
k=1
k=1
n
n
(c)
npx = np
x=1
x TRUE. x is dummy. n and p are free.
x=1
yx2 dx = y
(d)
x2 dx. TRUE. x
STATS 210
Tutorial 1
Model Answers
(a) Answer B: = cfw_ Toms phone calls . Events W , G, S, B, and L all describe
attributes of individual phone calls, so must be a set of phone calls.
(2)
(b) The rst statement is P(W ) = 0.2 (given). The other four are:
Statistics 210 FC
Assignment 3
Due: 3PM, May 15th , 2015
1 Midvale School for the Gifted has two types of students: Guessers
and Swots. All Midvale tests consist of sets of questions with yes/no
answers. Guessers will simply answer yes or no to each quest
Statistics 210 FC
Assignment 2
Due: 3PM, April 24th , 2015
1 Answer the following questions:
a (2 marks) [Particular case] Assume that the sample space is =
cfw_s1 , s2 , s3 , s4 . We have that P(s1 ) = 5/12, P(s2 ) = P(s3 ) = 1/6
and P(s4 ) = 1/4. We den