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Statistics for Machine Learning > 2. Probability Distributions > Flashcards

2. Probability Distributions Flashcards

1
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

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2
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

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3
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

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4
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

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5
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

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6
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

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7
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

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8
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

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9
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

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10
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

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11
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

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12
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

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13
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

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14
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

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15
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

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16
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

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17
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

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18
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

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19
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

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20
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

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21
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

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22
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

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23
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

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24
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

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25
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

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26
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

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27
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

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28
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

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29
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

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30
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

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31
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

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32
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

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33
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

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34
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

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35
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

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36
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

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37
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

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38
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

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39
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

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40
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

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41
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

42
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

43
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

44
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

45
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

46
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

47
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

48
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

49
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

50
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

51
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

52
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

53
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

54
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

55
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

56
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

57
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

58
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

59
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

60
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

61
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

62
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

63
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

64
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

65
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

66
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

67
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

68
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

69
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

70
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

71
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

72
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

73
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

74
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

75
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

76
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

77
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

78
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

79
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

80
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

81
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

82
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

83
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

84
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

85
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

86
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

87
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

88
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

89
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

90
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

91
Q

What is a Bernoulli distribution?

A

A discrete probability distribution for a single trial with two possible outcomes.

92
Q

What is the PMF of a Bernoulli(p) distribution?

A

P(X=1) = p, P(X=0) = 1 - p.

93
Q

What is a Binomial distribution?

A

A distribution representing the number of successes in n independent Bernoulli trials.

94
Q

What is the expected value of a Binomial(n, p) distribution?

A

E[X] = np.

95
Q

What is the variance of a Binomial(n, p) distribution?

A

Var(X) = np(1-p).

96
Q

What is the Poisson distribution used for?

A

Modeling the number of occurrences in a fixed interval given an average rate.

97
Q

What is the expected value of a Poisson(λ) distribution?

A

E[X] = λ.

98
Q

What is the standard deviation of a Poisson(λ) distribution?

A

sqrt(λ).

99
Q

What is a Uniform distribution?

A

A distribution where each outcome in an interval has equal probability.

100
Q

What is the CDF of a Uniform(a, b) distribution?

A

F(x) = (x - a) / (b - a) for a ≤ x ≤ b.

Statistics for Machine Learning (9 decks)

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