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Inform theory
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Questions in this quiz (81)
1What is the Hamming distance between two strings of equal length?
- Athe number of positions at which the corresponding symbols are different.
- Bq
2How does a noise affect the data?
- Adamage to the storage medium, frequency and phase characteristics of the communication
channel, failure of carriers - Ba
- Adamage to the storage medium, frequency and phase characteristics of the communication
3A bottle contains 8 marbles: 3 are red and 5 are blue. You are to take a marble
from the bottle without looking. What is the probability that you will pick a red marble?- A3/8
- B5/8
- C1/3
- D3/5
4What is the sample space for sum of two dice?
- A{7,8,9,10,11,12}
- B{2,3,4,5,6,7,8,9,10,11,12}
- C{1,2,3,4,5,6,7,8,9,10,11,12}
- D{1,2,3,4,5,6}
5 What is the sample space of one coin toss?
- A{H}
- BNone of the given
- C{H, T}
- D{T}
6How many elements are in the sample space of rolling one die?
- A36
- B12
- C6
- D24
7A die is rolled. What is the probability that the number rolled is greater than 2 and
even?- A5/6
- B1/3
- C1/2
- D2/3
8Among twenty-five articles, nine are defective, six having only minor defects and
three having major defects. Determine the probability that an article selected at
random has major defects given that it has defects.- A3/9 = 1/3
- BA
9Which of the following is NOT a possible probability?
- A1.25 (it is bigger than 1)
- BB. 0
- CC. 25/100
- DD. 1
10Find the probability of “o” symbol in “Morocco” word.
- A3/7
- B3
- C1/7
- D1
11You should encode a text which consists of 2 symbols with probabilities p(x1) =
0,05 and p(x2) = 0,95. What type of code is the most effective?- AA. Hartley’s code
- BB. Usual Shannon-Fano’s code
- CC. Block Shannon-Fano’s code
- DD. ASCII code
12You should encode a text which consists of 2 symbols with probabilities p(x1) =
0,2 and p(x2) = 0,8. What type of code is the most effective?- AB. Usual Shannon-Fano’s code
- BC. Block Shannon-Fano’s code
- CD. ASCII code
- DA. Hartley’s code
13Convert the message into a signal suitable for transmission over the channel of
communication, referred to us- AA. Redundancy
- BB. Decoding
- CC. Encoding
- DD. Entropy
14In case of Huffman coding we write … for a branch with a higher value?
- A1
- B2
15You should encode x1 and x2 symbols with block coding. Which blocks should be
involved in the coding?- AA. x1x2, x2x1
- BB. x1, x2
- CC. x1, x2, x1x2
- DD. x1x2,x2x1,x1x1,x2x2
16Choose the formula to calculate the probability in case of block coding.
- AP(x1x2) = Р(х1)*P(x2)
- B1
17A box contains 1 red, 2 yellow and 4 blue balls. You draw one ball. How many
different outcomes of this event are possible?- AA. 1
- BB. 7
- CC. 2
- DD. 3
18A box contains 2 red and 4 black balls. You draw one ball. How many different
outcomes of this event are possible?- A2
- B1
19Let the information capacity of one symbol is 1 bit and number of symbols in this
alphabet is 16. Compute economy of this language.- AA. 1/4
- B1
20Can entropy be negative?
- AA. Yes
- BB. Yes, but rarely
- CC. No
21When entropy is equal to 0?
- AЭнтропия равна 0, если вероятность одного из состояний источника информации равна 1,
и тем самым состояние источника полностью определено (вероятности остальных
состояний источника равны нулю, т.к. сумма вероятностей должна быть равна 1). - Bq
- AЭнтропия равна 0, если вероятность одного из состояний источника информации равна 1,
22An amount of information per one message element (symbol)?
- AA. Entropy
- BB. Min amount of information
- CC. None of the above
- DD. Max amount of information
23Events have the same probabilities. Choose the formula to determine the amount
of information.- AA. Hartley’s formula
- BB. Shannon’s formula
- CC. Bayes’ formula
- DD. Fano’s formula
24A message has 7200 bytes of information and fills in 4 pages with 40 lines. How
many symbols in one line? An alphabet consists of 64 symbols.- AA. 60
- B1
25A message has 3 Kb of information. An alphabet consists of 16 symbols. Find the
number of symbols in the message.- A6144
- B1
26A message with amount of information = 3 Kb contains 3072 symbols. Find the
number of symbols in the alphabet.- AA. 256
- B1
27Let an alphabet consists of 32 symbols. Find Imax in message with length = 6
symbols.- AA. 32
- BB. 30
- CC. 6
- DD. 24
28Choose the non-uniform code.
- AA. Bayees’
- B. Hartley
- CC. ASCII
- DD. Shannon-fano
29What is uniform code?
- AB. Coding in the binary system
- BC. None of the above
- CD. All code words have the different lengths and the same probability
- DA. All code words have the same length
30Find the information capacity of symbol from alphabet composed of 3 symbols?
All symbols are equiprobable.- AA. I = log23
- BB. I = 3 * log23
- CC. I = log32
- DD. I = (log23)/3
31 Find the information amount of a symbol from Kazakh language.
- AA. I = 42 * log 422
- BB. I = log242
- CC. I = log422
- DD. I = 42 * log242
32Find the information amount of symbol from Greek language(the number of
symbols is 24).- AA. I = 24 * log224
- BB. I = log224
- CC. I = 24 * log242
- DD. I = log212
33What are min and max values for conditional entropy H(Y|X)?
- AA. 0; 1
- BB. - H(Y); 0
- CC. 0; H(Y)
- DD. - H(Y); H(Y)
34. H = - ∑(pi*log pi). Call the formula.
- AA. Hartley’s formula to determine an entropy
- BB. Formula to determine the probability
- CC. Formula to determine a conditional entropy
- DD. Shannon’s formula to determine an entropy
35How does the increase of information affect on the level of entropy?
- AA. Has no effect
- BB. Decreases the entropy
- CC. Increases the entropy
36What is the meaning of number “2” in the formula I = n*log2m?
- AA. Information is measured in nits
- BB. It hasn’t any meaning
- CC. Binary number system
- DD. Message length equals to 2
37 Choose condition of an optimal coding (p - probability, l - length of a code word)
- AA. pi > pj and li <= lj
- BB. None of the given
- CC. pi < pj and li <= lj
- DD. pi > pj and li >= lj
38. Choose the method for optimal coding.
- A Shannon-Fano code or Huffman code
- Ba
39What is the first step of Shannon-Fano and Huffman coding?
- AA. Characters of the original alphabet are setted in descending order of probability
- BB. For all characters (letters) of the top subset assign a code element 0, and for characters
of the lower subset the 1 code - CC. Letters divided to the two subsets so that the overall probability of these subsets were
about equal - DD. For all characters (letters) of the top subset assign a code element 1, and for characters
of the lower subset the 0 code
40Choose the formula to determine an average length of codewords.
- AA. qavr = ∑ (pi/qi)
- BB. qavr = ∑ qi/n
- CC. qavr = ∑ pi/n
- DD. qavr = ∑ (pi*qi)
41 What should be done to determine if the code is optimal?
- AB. To check that all the characters in the text are encoded
- BA. To determine qAV
- CD. To compare the average length of code words and the entropy
- DC. To determine H
42What ratio should be done to call a code optimal?
- AA. (Length)gср = Н
- B1
43How many digits of codeword are required to encode 32 symbols of Russian
language?- AA. 5
- B1
44A box contained 2 white and 4 black balls. One white ball was drawn. Find the
probability of drawing a black ball.- AA. 1/5
- BB. 4/6
- CC. 1/6
- DD. 4/5
4540. A box contains 4 white and 5 black balls. Find the probability of drawing a white
ball.- AA. 4/9
- BB. 1/4
- CC. 5/9
- DD. 4/9
46Can the total entropy of two events be greater than 1?
- AA. Yes
- Bno
47We have 3 objects that have the same size but different mass x1, x2 and x3. Find
the entropy of drawing the heaviest of them. You can compare weights of objects only in
pairs- AA. 1 bit
- BB. 2 bits
- CC. 1.5 bits
- DD. 3 bits
48Choose the formula of the Chain rule:
- AA. None of the given
- BB. P(A|B) = [P(B|A)][P(A)]/P(B)
- CC. H(Y|X) = H(X,Y) + H(X)
- DD. H(Y|X) = H(X,Y) - H(X)
49H(A/B) = H(A) + HA(B). What is HA(B)?
- AA. Conditional entropy of event B in case that an event A occurred
- Ba
50. Choose the right property of joint entropy:
- AA. H(X, Y) <= H(X) + H(Y)
- BB. None of the given
- CC. H(X,Y) >= H(X)
- DD. All of the given
51Entropy doesn’t depend on the particular values of the random variable. Is this a
true statement?- AA. Yes
- Bno
52Let the information capacity of one symbol in Russian is about 1 bit. Compute
economy of the Russian language.- AA. 1/5 = 0.2
- Bb
53Let the information capacity of one letter in Russian is about 1 bit. Compute
redundancy of the Russian language.
Solution:
Imax = log32 = 5
S = 1-1/5 = 4/5 = 0.8 = 80%- AA. 1
- BB. 5
- CC. 0.2
- DD. 0.8
54Choose the formula to determine the redundancy S of a code.
- AA. S = 1 + E
- BB. E = Imax/Iavr
- CC. E = Iavr/Imx
- DD. S = 1-E
55 Entropy is maximum when…
- AA. None of the above
- BB. Probability of events is 1
- CC. Probabilities of events are different
- DD. Events are equiprobable
56. Probabilities of events are different. Choose the formula to determine the amount
of information.- AA. Hartley’s formula
- BB. Shannon’s formula
- CC. Bayes’ formula
- DD. Fano’s formula
57Let an asymmetrical tetrahedral pyramid is tossed. Probabilities of faces are
following: p1=1/2, p2=1/4, p3=1/8, p4=1/8. What’s the amount of information of this event?- AI = n * H => I = 4 * 1.75 = 6
- B1
58A message is written by characters of 16-character alphabet and contains 30
characters. What’s the amount of information in this message?- AA. 480
- BB. 120
- CC. 30
- DD. 16
59A message is written by characters of 4-character alphabet and contains 5
characters. What’s the amount of information in this message?- AA. 5
- BB. 10 [5*log2(4)]
- CC. 4
- DD. 2
60. A message is written by characters of 4-character alphabet and contains 30
characters. What’s the amount of information in this message?- AA. [ (n*log2(m)) = 30*log2(4) = 60 ]
- Bй
61Choose the Hartley’s formula to determine the entropy:
- AA. H = -∑(log pi)
- BB. H = -∑(pi * log pi)
- CC. H = -∑ pi
- DD. H = -∑(pi /log pi)
62Choose the Shannon's formula to determine the entropy:
- AA. H = -∑(log pi)
- BB. H = -∑(pi * log pi)
- CC. H = -∑ pi
- DD. H = -∑(pi /log pi)
63What is a measure of uncertainty?
- AA. Encoding
- BB. Entropy
- CC. Information
- DD. Redundancy
64Formula for calculating the entropy for m equiprobable events:
- AA. H = log m
- BB. P = m/n (n - number of events)
- CC. H = m*n (n - number of events)
- DD. P = 1/m
65What is 1 nit?
- AA. Unit of information with base = 16
- BB. Unit of information with base = 2
- CC. Unit of information with base = 10
- DD. Unit of information with base = e
66. What is 1 dit?
- AA. Decimal unit of information
- BB. Unit of information equal to 10 bits
- CC. Unit of information equal to 0.1 bit
- DD. Unit of information equal to 1 bit
67Choose the unit of information
- AA. Bit
- BB. Np
- CC. dB
- DD. None of the given
68Choose the unit of information
- AA. Bit
- BB. Nit
- CC. Dit
- DD. All of given
69Choose the formula for Bayes’ theorem
- AA. P(A|B) = [P(B|A)][P(A)] * P(B)
- BB. P(B|A) = P(A and B) * P(A)
- CD. P(B|A) = P(A and B) / P(A)
- DC. P(A|B) = [P(B|A)][P(A)] / P(B)
70Choose the formula for calculating a conditional probability
- AA. P(A|B) = [P(B|A)][P(A)] * P(B)
- BB. P(B|A) = P(A and B) * P(A)
- CC. P(A|B) = [P(B|A)][P(A)] / P(B)
- DD. P(B|A) = P(A and B) / P(A)
71Let the I average is 2 bits and number of symbols in this alphabet is 16. Compute
redundancy of this language- AA. 0.25
- BB. 1/8
- CC. 0.75
- DD. 0.5
1-2/4=0.5
72 This function determines an amount of information:
- AA. l = n*log m
- BB. l = m*n
- CC. l = log (m/n)
- DD. l = log (m*n)
73All of N messages are equiprobable. What is the probability p of a particular
message?- AA. P = 1/N
- BB. P = log(1/N)
- CC. P = N
- DD. P = log N
74Let the message source alphabet consists of m characters, each of which can be
an element of the message. What is the number N of possible messages with length n?- AA. N = log m
- BB. N = m*n
- CC. N = nm
- DD. N=m
757. An English teacher gave her class two tests. 15% of the class passed both tests
and 54% of the class passed the first test. What percent of those who passed the first
test also passed the second test?- AA. 27,7%
- B1
76In New England, 84% of the houses have a garage and 65% of the houses have a
garage and a back yard. What is the probability that a house has a backyard given that it
has a garage?- AB. 86%
- BA. 65%
- CC. 55%
- DD. 77%
77In Europe, 88% of all households have a television. 51% of all households have a
television and a VCR. What is the probability that a household has a VCR given that it
has a television?- AA. 58%
- BC. 173%
- CD. 27
- DB. 42%
78In New York State, 48% of all teenagers own a skateboard and 39% of all teenagers
own a skateboard and roller blades. What is the probability that a teenager owns roller
blades given that the teenager owns a skateboard?- AA. 29%
- BB. 81%
- CC. 87%
- DD. 123%
793. A number from 1 to 11 is chosen at random. What is the probability of
choosing an odd number?- AA. 5/11
- BB. 6/11
- CC. 1/2
- DD. 1/11
80A single 6-sided die is rolled. What is the probability of rolling an even number?
- AA. 1/2
- BB. 1/4
- CC. 1/3
- DD. 1/5
81A spinner has 3 equal sectors colored blue, green and red. What are the chances
of landing on blue after spinning the spinner?- AA. 3
- BB. 1/3
- CC. 1
- DD. 1/4
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- Quiz on Inform theory, created by Бибарыс Давренов on 13/03/2018.
- Author
- Бибарыс Давренов
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- English
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