Mathematical Science Syllabus Paper 2 Unit 29 To 34
29. Time-Series Analysis: Discrete-parameter stochastic processes; strong and weak stationarity; autocovariance and autocorrelation. Moving average, autoregressive, autoregressive moving average and autoregressive integrated moving average processes. Box-Jenkins models. Estimation of the parameters in ARIMA models; forecasting. Periodogram and correlogram analysis.
30. Stochastic Processes: Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution; branching processes; Random walk; Gambler's ruin. Markov processes in continuous time; Poisson processes, birth and death processes, Wiener process.
31. Demography and Vital Statistics: Measures of fertility and mortality, period and Cohort measures.
Life tables and its applications; Methods of construction of abridged life tables. Application of stable population theory to estimate vital rates. Population projections. Stochastic models of fertility and reproduction.
32. Industrial Statistics: Control charts for variables and attributes; Acceptance sampling by attributes; single, double and sequential sampling plans; OC and ASN functions, AOQL and ATI; Acceptance sampling by varieties. Tolerance limits. Reliability analysis: Hazard function, distribution with DFR and IFR; Series and parallel systems. Life testing experiments.
33. Inventory and Queueing theory: Inventory (S,s) policy, periodic review models with stochastic demand. Dynamic inventory models. Probabilistic re-order point, lot size inventory system with and without lead-time. Distribution free analysis. Solution of inventory problem with unknown density function. Warehousing problem. Queues: Imbedded markov chain method to obtain steady state solution of M/G/1, G/M/1 AND M/D/C, Network models. Machine maintenance models. Design and control of queueing systems.
