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Below I've given detailed information regarding the topics I wish to study, kindly suggest most appropriate book(s) :

Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes' theorem and independence of events.

Random Variables: Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev's inequality.

Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.

Joint Distributions: Joint, marginal and conditional distributions. Distribution of functions of random variables. Joint moment generating function. Product moments, correlation, simple linear regression. Independence of random variables.

Sampling distributions: Chi-square, t and F distributions, and their properties.

Limit Theorems: Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).

Estimation: Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.

Testing of Hypotheses:Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.

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    $\begingroup$ I see that this question has already received two close votes with the reason being that the question is "Too Broad." I disagree---it appears that So Lo is looking for a textbook that covers the material that might be seen in an advanced undergraduate course in statistics. So Lo: If that is the case, perhaps you could make that more clear at the top of your question? $\endgroup$
    – Xander Henderson
    Jul 6, 2018 at 17:20
  • $\begingroup$ @XanderHenderson Thank you. I am a bit confused to see the down votes $\endgroup$
    – So Lo
    Jul 6, 2018 at 17:23
  • $\begingroup$ math.stackexchange.com/q/315075/321264, math.stackexchange.com/q/51785/321264 $\endgroup$ Dec 27, 2020 at 15:48

2 Answers 2

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Degroot and Schervish covers all of that material rather well.

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Probability and Statistics - Hogg and Craig. This was our reference book for the probability and statistics undergraduate course.

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