ISI Kolkata Solved Question Papers

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Here is the exam paper

Consider a machine with three components whose times to failure are independently distributed as exponential random variables with mean . The machine continues to work as long as at least two components work. Find the expected time to failure of the machine.

A pin whose centre is xed on a at table is randomly and independently spun twice. Each time, the nal position is noted by drawing a line segment.

(a) What is the probability that the smallest angle between the two segments is more than half of the largest angle ?

(b) What is the probability that at least one of the two segments makes an angle which is less than 45 with the x-axis (when measured in the anti-clockwise direction) ?

Syllabus for Statistics and Probability

Probability and Sampling Distributions: Notions of sample space and probability. Combinatorial probability. Conditional probability and independence. Random variables and expectations. Moments and moment generating functions. Standard univariate discrete and continuous distributions. Joint probability distributions. Multinomial distribution. Bivariate normal and multivariate normal distributions. Sampling distributions of statistics. Weak law of large numbers. Central limit theorem.

Descriptive Statistics: Descriptive statistical measures. Contingency tables and measures of association. Product moment and other types of correlation. Partial and multiple correlation. Simple and multiple linear regression.

Statistical Inference: Elementary theory of estimation (unbiasedness, minimum variance, suciency). Methods of estimation (maximum likelihood method, method of moments). Tests of hypotheses (basic concepts and simple applications of Neyman-Pearson Lemma). Condence intervals. Inference related to regression. ANOVA. Elements of nonparametric inference.



ISI Kolkata Solved Question Paper







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