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Unit 1
1.Half-range Sine and cosine series
2.Root mean square value
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3.Harmonic Analysis( table sums in Fourier harmonic )
1.Fourier integral theorem
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2.Sine and cosine transform
3, Convolution theorem
1.Binomial, Poisson, Exponential and Normal distributions
2. Discrete and continuous random variables
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1. Covariance,Correlation . Linear regression **
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2.  Central limit theorem**
1.Differences between means, variations and ratio of two variances
2.Robustness .Method of moments

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**Very important questions are bolded and may be asked based on this topic

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Contact uS for more updates *These questions are expected for the exams This may or may not be asked for exams
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UNIT I FOURIER SERIES Dirichlet’s conditions – General Fourier series – Odd and even functions – Half-range Sine and cosine series – Root mean square value - Parseval’s identity – Harmonic Analysis. UNIT II FOURIER TRANSFORM Fourier integral theorem – Fourier transform pair - Sine and cosine transforms – Properties – Transform of elementary functions – Convolution theorem – Parseval’s identity. UNIT III RANDOM VARIABLES Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions - Functions of a random variable. UNIT IV TWO-DIMENSIONAL RANDOM VARIABLES Joint distributions – Marginal and conditional distributions – Covariance – Correlation and Linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables). UNIT V ESTIMATION THEORY Unbiased estimators - Efficiency - Consistency - Sufficiency - Robustness - Method of moments - Method of maximum Likelihood - Interval estimation of Means - Differences between means, variations and ratio of two variances.

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