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Probability Distributions & Sampling (Statistics) Solved Questions & Notes (2026) - Apex Rankers

Statistics & Data Science > Statistics > Probability Distributions & Sampling

4 Total Solved Questions
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Probability Distributions & Sampling

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Q. 1 Statistics
Difficulty: Hard (1 Mark)
How do changes in disease prevalence affect Positive Predictive Value (PPV) and Negative Predictive Value (NPV)?
A
Higher prevalence increases PPV and decreases NPV, while test Sensitivity and Specificity remain unchanged
✓ Correct
B
Higher prevalence increases both Sensitivity and PPV
C
Prevalence has no mathematical impact on predictive values
D
Higher prevalence decreases PPV and increases NPV
💡 Step-by-Step Explanation & Concept Rationale
Unlike sensitivity and specificity (intrinsic test properties), predictive values depend heavily on disease prevalence. As prevalence rises, True Positives increase relative to False Positives, increasing PPV, while NPV decreases.
Q. 2 Statistics
Difficulty: Medium (1 Mark)
What distribution describes the survival time of medical patients when the instantaneous hazard rate (failure rate) is constant over time?
A
Exponential Distribution
✓ Correct
B
Normal Distribution
C
Weibull Distribution with shape parameter > 1
D
Beta Distribution
💡 Step-by-Step Explanation & Concept Rationale
The exponential distribution is the only continuous distribution with a constant failure/hazard rate (memoryless property: h(t) = lambda). When hazard changes with time, the Weibull distribution is used.
Q. 3 Statistics
Difficulty: Hard (1 Mark)
In survival analysis and medical statistics, what is Cox Proportional Hazards Regression model used for?
A
Semi-parametric regression modeling time-to-event outcomes with multiple covariates without assuming a baseline hazard distribution
✓ Correct
B
Classifying images into medical diagnosis categories
C
Predicting mean blood pressure using ordinary least squares
D
Modeling count data with excessive zeros
💡 Step-by-Step Explanation & Concept Rationale
The Cox proportional hazards model is semi-parametric: it assumes covariate effects multiply the baseline hazard by exp(beta * X), but leaves the baseline hazard function h_0(t) completely unspecified.
Q. 4 Statistics
Difficulty: Medium (1 Mark)
In randomized clinical trials, what does 'Intention-to-Treat' (ITT) analysis dictate?
A
All participants are analyzed according to the group they were originally randomly assigned, regardless of compliance or dropouts
✓ Correct
B
Only participants who completed 100% of prescribed medication doses are analyzed
C
Patients who switched treatment groups are re-assigned to the new group
D
Non-compliant patients are permanently deleted from sample calculations
💡 Step-by-Step Explanation & Concept Rationale
Intention-to-treat (ITT) analysis preserves the benefits of randomization, prevents attrition bias, and mirrors real-world effectiveness by analyzing every subject in their originally assigned trial arm.
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