⏳ 3.5–4 months 🧠 Theory + PYQs 📝 Weekly Mocks

How to use ⚡

Follow week by week. Each day: 3h theory → 4h practice → 1h revision. Do PYQs alongside topics. Take a mock at the end of each module and fix mistakes the next day.

Focus: Master PDFs/MGFs

Week 5 · Matrices & Determinants

• Rank/nullity, systems, Cramer’s rule, row‑echelon forms.
• Eigenvalues/vectors, Cayley‑Hamilton, quadratic forms & definiteness.
• Practice: 20 matrix PYQs/day + 5 proofs/derivations per week.

Week 6 · Discrete RVs

• Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, Hypergeometric.
• Expectation, variance, MGFs; limiting/approximation relations.
• Daily: 25 PYQs + 5 transformation problems.

Week 7 · Continuous RVs

• Uniform, Exponential (memoryless), Gamma/Beta, Normal, Cauchy, Weibull distribution.
• Quantiles, mode/median/mean contrasts, MGFs & properties.
• Drill: Normal approximations + tail bounds (Chebyshev/Markov).

Week 8 · Multivariate + Bivariate Normal

• Joint/marginal/conditional cdf-pdf-pmf; independence; Jacobian transforms.
• Covariance, correlation; multinomial; additive properties via MGFs.
• Bivariate Normal: marginals/conditionals, correlation structure.
• Mock‑Full: Syllabus till Week 8 + review day.

Focus: Derivations + Speed

Week 9 · Limit Theorems + Sampling

• Convergences (in prob/mean square/a.s./in dist) & relations.
• WLLN, SLLN (idea), Borel-Cantelli lemma, Slutsky’s lemma, Delta method with CLT (i.i.d., finite variance).
• χ², t, F: definitions, pdf derivations via MGF, properties & relations.

Week 10 · Estimation

• Unbiasedness, sufficiency (factorization), completeness, UMVUE.
• Rao–Blackwell, Lehmann–Scheffé; Cramér–Rao bound & efficiency.
• MoM, MLE (invariance), LS for simple regression; CIs (Normal/2‑Normal/Exponential).
• Basu’s theorem, completeness of exponential family, ancillary statistics.

Week 11 · Testing of Hypotheses

• Null/alt (simple/composite), Type I/II, size, power, p‑value.
• NP Lemma; MP/UMP tests for one‑parameter families.
• LR tests for Normal parameters; structured PYQ set.
• UMP Unbiased tests, large sample tests, MLR property.

Week 12 · Nonparametrics + Stochastic Processes

• Runs test, EDF & KS (1‑sample), sign tests, Mann–Whitney.
• DTMC: TPM, higher‑order probs, classes, stationary/limiting dists.
• Poisson process: properties; interarrival & waiting times.
• Mock‑Full: Inference‑centric + review day.

Focus: Mixed Sets + Speed

Week 13 · Math + Prob Basics

• GOF tests (Chi-square) + Wilcoxon signed rank, Kendall rank correlation.
• All calculus + sequences; probability axioms & Bayes.
• Mock 1: Math‑heavy; make error log → fix next day.

Week 14 · Distributions (Uni + Multi)

• Introduce Regression Analysis (simple + multiple regression, Gauss–Markov, Fisher–Cochran).
• All discrete/continuous + transformations + BVN.
• Mock 2: Distribution & sampling heavy.

Week 15 · Estimation + Testing + Nonparametrics

• Multivariate Analysis (Hotelling’s T², Wishart, partial correlation).
• All theorems (RB, LS) + CRLB; MP/UMP/ LR tests; NP methods.
• Mock 3: Inference‑heavy; speed + accuracy.

Week 16 · Grand Revision

• extra stochastic processes: birth–death, Brownian motion.
• Formula walls, flashcards, mistake‑list drilling.
• 3–4 grand mocks in exam conditions; last 48h = light recap only.

• Finish assigned theory (with at least 1 handwritten page of formulas).
• ≥ 150 practice Qs (mix of PYQs + new). Accuracy ≥ 75%.
• 1 timed mock + 1 error‑correction session next day.
• Update mistake list (concept, trigger, fix) — revisit every Sunday.

• Parallel PYQs: Solve PYQs of the topic you studied the same day.
• Transformations first: For multi‑var, master Jacobians early.
• MGF toolbox: Many proofs become 2‑step with MGFs — practice them.
• Speed blocks: 25‑minute sprints + 5‑minute breaks (Pomodoro).