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Flashcards in Teorifrågor matstat Deck (25)
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1

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

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

2

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 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

3

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

Area

4

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.

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

5

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?

No

6

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?

No

7

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

It is better to use

1 Standard deviation;
2 Mode;
3 IQR

IQR

8

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 no, because it is not a repeatable experiment;

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

9

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 That the observed elementary outcome is an element of E;

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

10

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

All of these

11

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 No relation
b P(B|A)>P(B)

12

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)

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

13

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

4 forming a partition of the sample space

14

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

8. 2 and 3

15

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

3. a function on the sample space

16

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

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

17

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

4. Yes, because it can be viewed as an identical function on the sample space

18

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

4. [-2,2]

19

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

4. [0,4]

20

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

3. [0,2]

21

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

1. All real numbers

22

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)

5. [0,2)

23

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)

2. Bin(5,0.1)

24

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)

2. Bin(5,0.2)

25

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

1. Not suitable