2. Probability Distributions

Question 1

What is a Bernoulli distribution?

Answer 1

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

Question 2

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

Answer 2

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

Question 3

What is a Binomial distribution?

Answer 3

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

Question 4

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

Answer 4

E[X] = np.

Question 5

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

Answer 5

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

Question 6

What is the Poisson distribution used for?

Answer 6

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

Question 7

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

Answer 7

E[X] = λ.

Question 8

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

Answer 8

sqrt(λ).

Question 9

What is a Uniform distribution?

Answer 9

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

Question 10

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

Answer 10

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

Question 11

What is a Bernoulli distribution?

Answer 11

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

Question 12

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

Answer 12

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

Question 13

What is a Binomial distribution?

Answer 13

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

Question 14

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

Answer 14

E[X] = np.

Question 15

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

Answer 15

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

Question 16

What is the Poisson distribution used for?

Answer 16

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

Question 17

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

Answer 17

E[X] = λ.

Question 18

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

Answer 18

sqrt(λ).

Question 19

What is a Uniform distribution?

Answer 19

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

Question 20

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

Answer 20

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

Question 21

What is a Bernoulli distribution?

Answer 21

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

Question 22

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

Answer 22

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

Question 23

What is a Binomial distribution?

Answer 23

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

Question 24

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

Answer 24

E[X] = np.

Question 25

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

Answer 25

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

Question 26

What is the Poisson distribution used for?

Answer 26

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

Question 27

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

Answer 27

E[X] = λ.

Question 28

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

Answer 28

sqrt(λ).

Question 29

What is a Uniform distribution?

Answer 29

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

Question 30

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

Answer 30

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

Question 31

What is a Bernoulli distribution?

Answer 31

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

Question 32

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

Answer 32

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

Question 33

What is a Binomial distribution?

Answer 33

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

Question 34

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

Answer 34

E[X] = np.

Question 35

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

Answer 35

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

Question 36

What is the Poisson distribution used for?

Answer 36

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

Question 37

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

Answer 37

E[X] = λ.

Question 38

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

Answer 38

sqrt(λ).

Question 39

What is a Uniform distribution?

Answer 39

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

Question 40

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

Answer 40

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

Question 41

What is a Bernoulli distribution?

Answer 41

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

Question 42

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

Answer 42

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

Question 43

What is a Binomial distribution?

Answer 43

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

Question 44

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

Answer 44

E[X] = np.

Question 45

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

Answer 45

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

Question 46

What is the Poisson distribution used for?

Answer 46

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

Question 47

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

Answer 47

E[X] = λ.

Question 48

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

Answer 48

sqrt(λ).

Question 49

What is a Uniform distribution?

Answer 49

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

Question 50

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

Answer 50

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

Question 51

What is a Bernoulli distribution?

Answer 51

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

Question 52

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

Answer 52

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

Question 53

What is a Binomial distribution?

Answer 53

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

Question 54

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

Answer 54

E[X] = np.

Question 55

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

Answer 55

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

Question 56

What is the Poisson distribution used for?

Answer 56

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

Question 57

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

Answer 57

E[X] = λ.

Question 58

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

Answer 58

sqrt(λ).

Question 59

What is a Uniform distribution?

Answer 59

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

Question 60

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

Answer 60

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

Question 61

What is a Bernoulli distribution?

Answer 61

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

Question 62

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

Answer 62

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

Question 63

What is a Binomial distribution?

Answer 63

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

Question 64

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

Answer 64

E[X] = np.

Question 65

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

Answer 65

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

Question 66

What is the Poisson distribution used for?

Answer 66

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

Question 67

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

Answer 67

E[X] = λ.

Question 68

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

Answer 68

sqrt(λ).

Question 69

What is a Uniform distribution?

Answer 69

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

Question 70

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

Answer 70

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

Question 71

What is a Bernoulli distribution?

Answer 71

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

Question 72

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

Answer 72

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

Question 73

What is a Binomial distribution?

Answer 73

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

Question 74

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

Answer 74

E[X] = np.

Question 75

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

Answer 75

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

Question 76

What is the Poisson distribution used for?

Answer 76

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

Question 77

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

Answer 77

E[X] = λ.

Question 78

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

Answer 78

sqrt(λ).

Question 79

What is a Uniform distribution?

Answer 79

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

Question 80

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

Answer 80

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

Question 81

What is a Bernoulli distribution?

Answer 81

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

Question 82

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

Answer 82

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

Question 83

What is a Binomial distribution?

Answer 83

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

Question 84

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

Answer 84

E[X] = np.

Question 85

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

Answer 85

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

Question 86

What is the Poisson distribution used for?

Answer 86

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

Question 87

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

Answer 87

E[X] = λ.

Question 88

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

Answer 88

sqrt(λ).

Question 89

What is a Uniform distribution?

Answer 89

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

Question 90

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

Answer 90

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

Question 91

What is a Bernoulli distribution?

Answer 91

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

Question 92

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

Answer 92

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

Question 93

What is a Binomial distribution?

Answer 93

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

Question 94

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

Answer 94

E[X] = np.

Question 95

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

Answer 95

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

Question 96

What is the Poisson distribution used for?

Answer 96

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

Question 97

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

Answer 97

E[X] = λ.

Question 98

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

Answer 98

sqrt(λ).

Question 99

What is a Uniform distribution?

Answer 99

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

Question 100

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

Answer 100

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