Probability And Statistics In Data Science Using Python Exam Solved -3

PROBABILITY AND STATISTICS IN DATA SCIENCE USING
PYTHON EXAM SOLVED #3

1.1 (T or F) Probability and Statistics provide mathematical tools for estimating the
likelihood of random events - correct answer True

1.1 Which of the following are best solved using probability and statistics?

A) Predicting the number of rainy days in April
B) Approximating the closing price of IBM stock tomorrow.
C) Estimating your potential winnings in a game of Blackjack.
D) Guessing the winner of the next World Cup. - correct answer A, B, C, D

1.1 What are probability and statistics useful for?

A) Quantifying Uncertainty
B) Finding exact solutions to mathematical equations.
C) Making Predictions about the future. - correct answer A & C

There is no uncertainty in B.

1.2 When the number of coin flips increases, the distribution of the sum of Heads (1)
and Tails (-1) becomes:

A) More concentrated around zero
B) Skewed to positive values
C) Skewed to negative values
D) More spread out across all possibilities - correct answer A. The randomness will
even out, and what we get is the average of -1 and 1 which is 0.

1.3 If we flip a coin a thousand times and get 507 heads, can we conclude with
certainity that the coin is unbiased? - correct answer No

1.3 In rolling a fair 6-sided die 1200 times, roughly how many times would you expect to
see a 2? - correct answer 200.

Because 1200 x 1/6 = 200.

1/6 is the probability to get a 2.

1.3 A coin is tossed 1000 times and turns up heads 700 times. Is the coin biased? -
correct answer Yes.

The probability that an ubiased coin would generate 700 heads is small. Hence we can
be confident that it is biased.

,1.3 Which of the following describes the differences between probability and statistics?

A) Probability predicts what will happen. Statistics, in part, uses what has already
happened.
B) Probability requires existing data. Statistics requires underlying models.
C) they're the same thing. - correct answer A

1.4 What is the probability of drawing a Queen from a deck of 52 cards? - correct
answer 4/52

1.4 (True or False) If we repeat an experiment many times, the long-term frequencies of
the outcomes converge to the probabiilities. - correct answer True

2.1 (T or F). The empty set is unique - correct answer True

2.1 (T or F) The universal set (Omega) is unique - correct answer False

2.1 Which of the following hold?

A) 0 exists {0, 1}
B) a exists {A, B}
C) {a, b} exists {{a, b}, c} - correct answer A and C

2.1 Recall that /zero/ is the empty set. How many elements do the following sets have?

1. /zero/
2. {/zero/}
3. {/zero/, /zero/}
4. {{/zero/}, /zero/} - correct answer 1. 0
2. 1
3. 1
4. 2

2.1 How many elements do the following sets have?

1. {a, b}
2. {{a, b}}
3.{{a, b}, {b, a}, {a, b, a}}
4. {a, b, {a, b}} - correct answer 1. 2
2. 1
3. 1
4. 3

2.1 Let A be the set of anagrams of singular English animal names. For example, "nails"
and "slain" are anagrams of "snail". So all three exist in A, yet "bar" does not exist in A.

,Which of the following exist in A?
1. Tan
2. Pea
3. Low
4. Bare
5. Loin
6. Bolster - correct answer All of the above

2.1 List the elements of the following sets

1. {a}
2. {{a}}
3. {a, {b}}
4. {/emptyset/}
5. /emptyset/ - correct answer 1. A
2. {a}
3. A, {b}
4. /emptyset/
5. None

2.2 How many elements are there in the real interval [2, 4) - correct answer Infinitely
many points: 2, 2.1, 2.11, 2.111, etc

2.2 Which of the following define a set unambiguously?

A) {3, 4, 5, 7}
B) {negative primes}
C) {good drivers in San Diego} - correct answer A & B

2.2 Which of the following are true?

1. 0 exists in {Even Numbers}
2. 0.5 exists in N
3. /emptyset/ exists in Q - correct answer 1.

2.2 Which of the following hold?

1. {0} = /emptyset/
2. {0, 1, 2} = {2, 0, 1, 1}
3. {{0}, 1} = {0, {1}} - correct answer 2.

2.2 Which of the following are true?

1. E exists in {1, 2, ..., 10}
2. Pi exists in (3, 3.5)
3. 2 exists in [-2, 2) - correct answer 2.

, 2.3 Visualizing Sets

A venn diagram for 2 sets has 4 regions, for three sets has 8 regions. How many
regions are there in a Venn diagram of 4 sets? - correct answer 16.

2.4 If S is a proper, or strict, subset of T, then:

1. S cannot be empty
2. T cannot be empty
3. S and T must intersect - correct answer 2.

2.4 Given the expression 'm exists in A', what can be said?

1. M belongs to A
2. A is a member of m
3. M is an element of the set A
4. M is a set of elements
5. A contains m - correct answer 1. 3. 5

2.4 Which of the following is not true

1. {red, green, blue} = {blue, red, green}
2. {1, 2, 3} contains 1
3. 2 exists in {all odd integers} - correct answer 3.

2.4 Which of the following holds

1. {3, 4} is not a proper superset of {3, 4}
2. {3, 4} != {3, 4}
3. {4, 3} is a proper subset of {3, 4}
4. {3, 4} is a proper subset of {4, 3} - correct answer 1.

2.4 Which of the following are subsets of A = [2, 4)

1. C = {2, 3, 4}
2. D = (2, 4)
3. E = /emptyset/ - correct answer 2 and 3

2.4 Let P(S) be the collection of all subsets of S, and Q(S) be the collection of all proper
subsets of S.
Which of the following hold for every set of S

1. P(S) is a subset of Q(S)
2. P(S) is a superset of Q(S)
3. P(S) is a proper subset of Q(S)