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Econometrics & Data Science

Probability Theory & Statistics 2

12 Topics 3 Free High Priority
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📍 Mastery Path
📊 Exam Intel Report
⚡ High Leverage Qs
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T1: Bivariate Foundations Done

Joint distributions, marginals, and independence for continuous random variables.

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T2: Conditional & Covariance Done

Conditional distributions, conditional expectation, covariance and correlation.

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3
T3: Non-Rectangular Supports In Progress

Integration over non-standard regions, careful limit setup, and common exam traps.

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T4: Transformations Locked

Change-of-variable technique, Jacobians, and distribution of functions of RVs.

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T5: Order Statistics Locked

Min/max distributions, k-th order statistic formula, joint distributions.

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T6: Sampling Distributions Locked

Chi-squared, t, and F distributions derived from first principles.

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15 MARKS ORDER STATISTICS MULTI-PART

A random sample of size n = 4 is drawn from f(x) = 2/x³ for x > 1. Find the PDF of the sample maximum, the expected value of the minimum, and the joint distribution of X(1) and X(4).

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12 MARKS TRANSFORMATIONS

Let X ~ Gamma(α, β). Using the CDF method, derive the distribution of Y = 2X/β and show it follows a chi-squared distribution...