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Matstat > Teorifrågor matstat > Flashcards

Teorifrågor matstat Flashcards

1
Q

Numerical data can be divided into two types: discrete and continuous.

Are these classes overlap, i.e. can a data be discrete and continuous type at the same time?

1 No;
2 Mathematically, no, but for analytical purposes it may be convenient to treat discrete data with a fine grid as continuous

A

2 Mathematically, no, but for analytical purposes it may be convenient to treat discrete data with a fine grid as continuous

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2
Q

The words above each answer box refer to a data attribute which can be associated with people’s activities.

Identify the type of each attribute; and enter 1 or 2 or 3 or 4 into the appropriate answer box:-

1 for nominal data, 2 for ordinal data, 3 for discrete numerical data, and 4 for continuous numerical data.

If the number of different possible (sensible) numerical values exceeds 20, then (for this question) respond with ‘4’ rather than ‘3’

a Number of goals scored in a football match

b Street you live in

c The time until the end of the class

d Disease incidence: epidemic, common, rare

e Community type : hamlet, village, town, city

A

a Number of goals scored in a football match
Discrete numerical data

b Street you live in
Nominal Data

c The time until the end of the class
Continuous numerical data

d Disease incidence: epidemic, common, rare
Ordinal data

e Community type : hamlet, village, town, city
Ordinal data

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3
Q

A histogram consists of rectangles with the bases spanning the range of the sample divided into disjoint regions: bins. Which measure of rectangles is proportional to the number of observations in the corresponding bins?

It is:

1 height
2 area
3 weight
4 none of these

A

Area

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4
Q

The Pie chart is considered as a bad presentation tool by serious statisticians.

This is because

1 it raises appetite;
2 statisticians are jealous of the bakers;
3 the humans are bad at comparing non-linear measures: areas of wedges in this case.

A

The humans are bad at comparing non-linear measures: areas of wedges in this case.

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5
Q

Robustness is the property of being (almost) insenitive to the presence of outliers.

Is the mean of the sample is a robust measure of the location of data?

1 Yes;
2 No;
3 Who cares?

A

No

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6
Q

Robustness is the property of being (almost) insenitive to the presence of outliers.

Is the IQR of the sample is a robust measure of the data variability?
1 Yes;
2 No;
3 Who cares?

A

No

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7
Q

Which measure of variability is preferable to use for highly skewed data?

It is better to use

1 Standard deviation;
2 Mode;
3 IQR

A

IQR

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8
Q

Is it possible to speak about probability that the 1st of January 2027 will be snowy?

a The answer is

1 yes, why not?;
2 no, because it is not a repeatable experiment;
3 I wish it does!

b How should one reformulate the question to make probabilistic sense to it?

1 It snows in Gothenburg on the 1st of January;
2 It always snows on the 1st of January;
3 It rains on the 1st of January 2017.

A

a no, because it is not a repeatable experiment;

b It snows in Gothenburg on the 1st of January;

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9
Q

What does it mean formally

a that an event E happens?

1 That the observed elementary outcome is an element of E;
2 That the observed elementary outcome is not an element of E;
3 That the observed elementary outcome is an element of the sample space

b that an event E does not happen?

1 That the observed elementary outcome is an element of E;
2 That the observed elementary outcome is not an element of E;
3 That the observed elementary outcome is an element of the sample space

A

a That the observed elementary outcome is an element of E;

b That the observed elementary outcome is not an element of E;

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10
Q

The rules of Probability concerning the unions and intersections of sets (events)

is similar to those of

1	length
2	area
3	volume
4	electrical charge
5	all of these
A

All of these

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11
Q

Let A and B be two events happening with positive probability.

a How do P(A) and P(A|B) compare?

1	No relation
2	P(A) > P(A|B)
3	P(A) < P(A|B)
4	P(A) = P(A|B)

What does P(A|B) > P(A) imply?

1	Nothing
2	P(B|A)
3	P(B|A)>P(B)
4	P(AB)=0
A 
a No relation
b P(B|A)>P(B)
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12
Q

Let A,B,C be events such that P(ABC) > 0.

What is P(ABC) always equal to?

1	0
2	1
3	P(A) P(B) P(C)
4	P(A|B) P(B|C) P(C|A)
5	P(A) P(B|A) P(C|AB)
A

5 P(A) P(B|A) P(C|AB)

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13
Q

Let B,C and D be events of positive probabilities.

For the Full Probability formula
P(A)=P(A|B)P(B)+P(A|C)P(C)+P(A|D)P(D)
to be true, it is necessary and sufficient that B,C,D are…

1	disjoint
2	covering the whole sample space
3	of equal probabilities
4	forming a partition of the sample space
5	independent
A

4 forming a partition of the sample space

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14
Q

Let positive probability events A and B be such that P(A|B)=P(A|Bc).

Which of the following are then true?

  1. P(A) = P(B)
  2. P(A) = P(A|B)
  3. A and B are independent
  4. P(B) = 1/2
1	Only 1
2	Only 2
3	Only 3
4	Only 4
5	1 and 2
6	1 and 3
7	1 and 4
8	2 and 3
9	2 and 4
10	3 and 4
11	All
12	None
A
  1. 2 and 3
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15
Q

What is a random variable?

In mathematical terms, a discrete random variable is

1 a variable which value is unknown
2 a variable which value is random
3 a function on the sample space
4 it is not a mathematical notion

A
  1. a function on the sample space
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16
Q

Assume that X is a discrete random variable on a sample space S and f is a continuous function on the real line R

Is f(X) a random variable?

1 Yes, because f(X) is also random
2 Yes, because composition of a function S to R and R to R is a function from S to R
3 No, because f is non-random
4 It depends on f and X

A

2 Yes, because composition of a function S to R and R to R is a function from S to R

17
Q

Is the constant a random variable?

1 No, because it is non-random
2 It depends on its value
3 Yes, because a constant can be random
4 Yes, because it can be viewed as an identical function on the sample space

A
  1. Yes, because it can be viewed as an identical function on the sample space
18
Q

A random variable X takes values in the interval [-2,2].

What is the possible range for its mean EX?

1	Any real number
2	all negative numbers
3	all positive numbers
4	[-2,2]
5	[-4,4]
6	only 0
A
  1. [-2,2]
19
Q

A random variable X takes values in the interval [-2,2].

What is the possible range for its variance var X?

1	Any real number
2	all positive numbers
3	[0,2]
4	[0,4]
5	only 0
A
  1. [0,4]
20
Q

A random variable X takes values in the interval [-2,2].

What is the possible range for its standard deviation?
1	Any real number
2	all positive numbers
3	[0,2]
4	[0,4]
5	only 0
A
  1. [0,2]
21
Q

The variance of a random variable X equals var X = 4. What is the possible range for its mean EX?

1	All real numbers
2	all negative numbers
3	all positive numbers
4	[-2,2]
5	[-4,4]
6	only 0
A
  1. All real numbers
22
Q

A random variable X is such that EX^2 <4. What is the possible range for its standard deviation s?

1	All real numbers
2	all nonnegative numbers
3	(-2,2)
4	(-4,4)
5	[0,2)
6	[0,4)
A
  1. [0,2)
23
Q

Among 1000 LED mini-lamps contained in a box there are 100 which are not working. A sample of 5 LEDs is taken at once. Is it suitable to use a Binomial distribution to describe the number of defective LEDs in the sample? If yes, then which parameters of this distribution?

1	Not suitable
2	Bin(5,0.1)
3	Bin(1000,0.1)
4	Bin(100,0.1)
A
  1. Bin(5,0.1)
24
Q

Among 10 LED mini-lamps contained in a box there are 2 which are not working. A sample of 5 LEDs is taken one LED by one: each time the taken lamp is returned to the box before the next one is taken. Is it suitable to use a Binomial distribution to describe the number of defective LEDs in the sample? If yes, then what are the parameters of this distribution?

1	Not suitable
2	Bin(5,0.2)
3	Bin(10,0.2)
4	Bin(5,0.1)
A
  1. Bin(5,0.2)
25
Q

Among 10 LED mini-lamps contained in a box there are 2 which are not working. A sample of 5 LEDs is taken at once. Is it suitable to use a Binomial distribution to describe the number of defective LEDs in the sample? If yes, then what are the parameters of this distribution?

1	Not suitable
2	Bin(5,0.2)
3	Bin(10,0.2)
4	Bin(5,0.1
A
  1. Not suitable

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