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Statistics with Python > Midterm > Flashcards

Midterm Flashcards

1
Q

Define population.

A

Entire set of objects of interest.

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2
Q

Define sample.

A

Subset of the set of objects of interest.

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3
Q

Distinguish between a designed experiment and an observational study.

A

Designed: Researcher exerts control over experiment. E.g. Placebo or drug
Observational: Observes and records variables of interest without interfering. E.g. Surveys

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4
Q

What is an explanatory variable?

A

A variable of interest being studied.

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5
Q

Define Quantitative Data. Another name?

A

Measurements that are recorded on a natural numerical scale. Numerical.

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6
Q

Distinguish between continuous and discrete.

A

Continuous: Fall anywhere on the real line.
Discrete: Take a finite set of values. E.g. Integers.

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7
Q

Define qualitative data. Another name?

A

Measurements that cannot be recorded on a natural numerical scale. Categorical.

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8
Q

Distinguish between nominal and ordinal data.

A

Nominal: No meaningful ordering.
Ordinal: Has an inherent order.

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9
Q

What are the three main graphical summaries used for?

A

Barchart: Shows the distribution of categorical values.
Histogram: Shows the distribution of numerical values.
Scatter Plot: Shows the relationship between variables.

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10
Q

What is a bin on a histogram?

A

The width of a bar.

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11
Q

Explain the box plot.

A

Median = The line inside the box.
1st Quartile = lower horizontal edge
3rd Quartile = higher horizontal edge
IQR = vertical edge.
Arms = 1.5(IQR) in both directions
Outliers = white dots outside arms.

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12
Q

What is an experiment?

A

An experiment is an act or process of observation that leads to one possible outcome with some randomness.

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13
Q

What is the sample space?

A

All the possible outcomes in an experiment.

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14
Q

What is an event?

A

An event is a collection of sample points from S. It is a subset of the Sample Space S.

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15
Q

What is the test for independence? Give another one.

A

P(A|B) = P(A) or P(B|A) = P(B)

P(A ∩ B) = P(A)P(B)

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16
Q

What is the multiplicative rule?

A

P(A ∩ B) = P(B|A)P(A)
= P(A|B)P(B)

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17
Q

Explain the partitioning principle.

A

Divides A into two cases.
A happening when B does
A happening when B doesn’t
P(A) = P(A|B)P(B) + P(A|B’)P(B’)

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18
Q

What is a random variable?

A

Is a variable which assumes numerical values representing the outcome of an experiment.

19
Q

What is discrete probability distribution function? Another name.

A

It gives the probability of each possible value that the random variable can assume:
P(X=x) equivls p(x).
probability mass function.

20
Q

What is the cumulative distribution function of a random variable X?

A

F(x) = P(X <= x) = u=0 sum x p(u)

21
Q

What is the formula for the mean / expected value of a discrete random variable?

A

sum of x (x * p(x))

22
Q

What is the expected value of a constant?

A

E[c] = c

23
Q

What is the multiplicative effect of a constant with expected values?

A

E[cX] = cE[X]

24
Q

What is the sum of random variables rules for expected value?

A

E[X1 + X2 + … + Xk] = E[X1] + … + E[Xk]

25
Q

Formula for variance.

A

variance = E(X^2) - E(X)^2

26
Q

What is the variance of a constant?

A

Var(c) = 0

27
Q

What is the variance of a constant times X?

A

Var(aX) = a^2Var(X)

28
Q

What is the variance of sum and subtraction in variance?

A

Var(X1 + … + Xm) = Var(X1 - … - Xm) = Var(X1) + … + Var(Xm)

29
Q

What is a hypergeometric experiment?

A

Drawing n elements at random from N objects without replacment. s are special items and N - s are regular items.
The hypergeometric random variable X counts the number of special items in a draw of n elements from N.

30
Q

Formula for P(X=x) for hypergeometric probability distribution.

A

=
(s choose x) * (N-s choose n-x) / (N choose n)

where N = total number of elements.
s = number of special items.
n = number of draws.

31
Q

Formula for expected value of X in a hypergeomtric distribution.

A

E[X] = mean = ns / N

where N = total number of elements.
s = number of special items.
n = number of draws.

32
Q

Formula for variance of X in a hypergeomtric distribution.

A

Var[X] = s.d.^2 = n * (s / N) * (N - s / N) * (N - n / N - 1)

where N = total number of elements.
s = number of special items.
n = number of draws.

33
Q

What is the key difference between binomial and hypergeometric trials?

A

Binomial: Independent trials.
Hypergeometric: No longer independent.

34
Q

What are poisson variables concerned with?

A

Number of times an event happens in a specified (time) period.

35
Q

What does the word period refer to in the definition of a poisson?

A

length, area, volume, time as long as it is fixed for the experiment.

36
Q

Define poisson random variables.

A
  1. The probability that the event occurs is the same for intervals of the same size.
  2. Intervals do not overlap.
37
Q

Give the formula for calculating the probability of a Poisson.

A

P(Y = y) = (lambda^y * e^(lambda * -1) / y factorial)

where lambda is the rate with which events occur in one unit.

38
Q

What is the mean and variance of a poisson?

A

E[Y] = lambda
Var[Y] = lambda

39
Q

Adding Poissons Rules?

A

X~Poisson(k) + Y~Poisson(n) = X + Y~Poisson(k + n)

40
Q

Formula for variance of binomial variable.
Formula for standard deviation of binomial variable.

A

np(1-p)
root(np(1-p))

41
Q

Formula for expected value of binomial variable.

A

np

42
Q

Define mutually exclusive?

A

Two events being mutually exclusive means they cannot occur at the same time or simultaneously. The probability of both the events happening is 0.

43
Q

Define independent?

A

When two events are mutually independent, it means that the occurrence of one event does not affect the probability of the other event occurring. The probability of both occurring is simply the probability of one occurring multiplied by the probability of the other.

44
Q

State and explain the central limit theorem.

A

States that the distribution of sample means from a large number of independent, identically distributed random variables will approximate a normal distribution, regardless of the original population distribution.

Statistics with Python (5 decks)

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