READ_ONLY_ACCESS
[
  {
    "id": "stats1-w01-000",
    "front": "Week 1 Diagnostic: Which scale of measurement applies to 'temperature measured in Celsius'?",
    "back": "Answer: C — Celsius has an arbitrary zero point (0°C does not mean total absence of heat), so it is an Interval scale. Ratios like 'twice as hot' are not meaningful on this scale."
  },
  {
    "id": "stats1-w01-001",
    "front": "Week 1 Diagnostic: Is the number of students attending a lecture a discrete or continuous numerical variable?",
    "back": "Answer: A — Student counts take distinct non-negative integer values (0, 1, 2, ...), making it a discrete numerical variable."
  },
  {
    "id": "stats1-w02-000",
    "front": "Week 2 Diagnostic: In a dataset of 50 students, 20 prefer Python, 15 prefer Java, and 15 prefer C++. What is the relative frequency of students who prefer Python?",
    "back": "Answer: 0.4 — Relative frequency = count / total = 20 / 50 = 0.4."
  },
  {
    "id": "stats1-w02-001",
    "front": "Week 2 Diagnostic: Which measure of central tendency is valid for nominal categorical data?",
    "back": "Answer: C — Nominal data has no ordering or numerical values, so only the most frequent category (Mode) is meaningful."
  },
  {
    "id": "stats1-w03-000",
    "front": "Week 3 Diagnostic: For the dataset [3, 7, 8, 5, 12, 14, 21, 13, 18], what is the median?",
    "back": "Answer: 12 — Sorted dataset: [3, 5, 7, 8, 12, 13, 14, 18, 21]. With n = 9, the median is the 5th element: 12."
  },
  {
    "id": "stats1-w03-001",
    "front": "Week 3 Diagnostic: If a distribution has a third quartile Q3 = 45 and a first quartile Q1 = 25, what is the Interquartile Range (IQR)?",
    "back": "Answer: 20 — IQR = Q3 - Q1 = 45 - 25 = 20."
  },
  {
    "id": "stats1-w04-000",
    "front": "Week 4 Diagnostic: What is the possible range of values for Pearson's correlation coefficient r?",
    "back": "Answer: B — Pearson's r is always bounded between -1 and +1 inclusive, where -1 indicates perfect negative linear correlation and +1 indicates perfect positive linear correlation."
  },
  {
    "id": "stats1-w04-001",
    "front": "Week 4 Diagnostic: If variables X and Y have a correlation coefficient r = 0, does that guarantee they are completely independent?",
    "back": "Answer: B — Pearson's r only measures linear relationships. Two variables can have a strong nonlinear relationship (e.g., Y = X^2 on [-1, 1]) and still yield r = 0."
  },
  {
    "id": "stats1-w05-000",
    "front": "Week 5 Diagnostic: A cafeteria offers 4 soups, 5 main courses, and 3 desserts. How many distinct meal combinations (1 soup, 1 main, 1 dessert) can a student choose?",
    "back": "Answer: 60 — By the Rule of Product: 4 * 5 * 3 = 60."
  },
  {
    "id": "stats1-w05-001",
    "front": "Week 5 Diagnostic: If 13 pigeons fly into 12 pigeonholes, at least one pigeonhole must contain at least how many pigeons?",
    "back": "Answer: 2 — By the Pigeonhole Principle, ceil(13 / 12) = 2."
  },
  {
    "id": "stats1-w06-000",
    "front": "Week 6 Diagnostic: In how many ways can a committee of 3 members be selected from a group of 7 candidates?",
    "back": "Answer: 35 — C(7, 3) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35."
  },
  {
    "id": "stats1-w06-001",
    "front": "Week 6 Diagnostic: In how many ways can 5 distinct books be arranged on a single shelf?",
    "back": "Answer: 120 — P(5, 5) = 5! = 120."
  },
  {
    "id": "stats1-w07-000",
    "front": "Week 7 Diagnostic: Two fair 6-sided dice are rolled. What is the probability that the sum of the faces equals 7?",
    "back": "Answer: A — Total outcomes = 36. Outcomes with sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) -> 6 outcomes. Probability = 6/36 = 1/6."
  },
  {
    "id": "stats1-w07-001",
    "front": "Week 7 Diagnostic: If events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.4, what is P(A or B)?",
    "back": "Answer: 0.7 — For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.3 + 0.4 = 0.7."
  },
  {
    "id": "stats1-w08-000",
    "front": "Week 8 Diagnostic: If P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2, are A and B independent?",
    "back": "Answer: A — P(A) * P(B) = 0.4 * 0.5 = 0.2. Since P(A and B) = P(A)*P(B), events A and B are independent."
  },
  {
    "id": "stats1-w08-001",
    "front": "Week 8 Diagnostic: What is P(A|B) if P(A and B) = 0.15 and P(B) = 0.30?",
    "back": "Answer: 0.5 — P(A|B) = P(A and B) / P(B) = 0.15 / 0.30 = 0.5."
  },
  {
    "id": "stats1-w09-000",
    "front": "Week 9 Diagnostic: For a discrete random variable X with PMF P(X=1) = 0.2, P(X=2) = 0.5, P(X=3) = 0.3, what is the value of the CDF F(2)?",
    "back": "Answer: 0.7 — F(2) = P(X <= 2) = P(X=1) + P(X=2) = 0.2 + 0.5 = 0.7."
  },
  {
    "id": "stats1-w09-001",
    "front": "Week 9 Diagnostic: Which of the following is NOT a property of a valid CDF F(x)?",
    "back": "Answer: C — A CDF is always non-decreasing and approaches 1 as x -> inf."
  },
  {
    "id": "stats1-w10-000",
    "front": "Week 10 Diagnostic: Let X take values 1 and 3 with probabilities 0.4 and 0.6 respectively. What is E[X]?",
    "back": "Answer: 2.2 — E[X] = 1*(0.4) + 3*(0.6) = 0.4 + 1.8 = 2.2."
  },
  {
    "id": "stats1-w10-001",
    "front": "Week 10 Diagnostic: If Var(X) = 4, what is Var(3X + 5)?",
    "back": "Answer: 36 — Var(aX + b) = a^2 * Var(X). Here a = 3, so Var(3X + 5) = 3^2 * 4 = 9 * 4 = 36."
  },
  {
    "id": "stats1-w11-000",
    "front": "Week 11 Diagnostic: If X follows a Binomial distribution with n = 10 and p = 0.3, what is E[X]?",
    "back": "Answer: 3 — For X ~ Bin(n, p), E[X] = n * p = 10 * 0.3 = 3."
  },
  {
    "id": "stats1-w11-001",
    "front": "Week 11 Diagnostic: For a Poisson random variable Y with parameter lambda = 4, what is the variance Var(Y)?",
    "back": "Answer: 4 — For Y ~ Pois(lambda), Var(Y) = lambda = 4."
  },
  {
    "id": "stats1-w12-000",
    "front": "Week 12 Diagnostic: For a continuous random variable X with PDF f(x), what is P(X = 5)?",
    "back": "Answer: 0 — For any continuous random variable, the probability of taking any exact single point value is strictly 0: P(X = c) = 0."
  },
  {
    "id": "stats1-w12-001",
    "front": "Week 12 Diagnostic: If X is uniformly distributed on [2, 6], what is the value of the PDF f(x) for x in [2, 6]?",
    "back": "Answer: 0.25 — For X ~ U(a, b), f(x) = 1 / (b - a). Here b = 6, a = 2, so f(x) = 1 / (6 - 2) = 1/4 = 0.25."
  }
]