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Syllabus:-
| Sr. No. | Content | Total Hrs | % Weightage |
|---|---|---|---|
| 01 | Basic Probability: Experiment, definition of probability, conditional probability, independent events, Bayes' rule, Bernoulli trials, Random variables, discrete random variable, probability mass function, continuous random variable, probability density function, cumulative distribution function, properties of cumulative distribution function, Two dimensional random variables and their distribution functions, Marginal probability function, Independent random variables. |
08 | 20 % |
| 02 | Some special Probability Distributions: Binomial distribution, Poisson distribution, Poisson approximation to the binomial distribution, Normal, Exponential and Gamma densities, Evaluation of statistical parameters for these distributions. |
10 | 25 % |
| 03 | Basic Statistics: Measure of central tendency: Moments, Expectation, dispersion, skewness, kurtosis, expected value of two dimensional random variable, Linear Correlation, correlation coefficient, rank correlation coefficient, Regression, Bounds on probability, Chebyshev‘s Inequality |
10 | 20 % |
| 04 | Applied Statistics: Formation of Hypothesis, Test of significance: Large sample test for single proportion, Difference of proportions, Single mean, Difference of means, and Difference of standard deviations. Test of significance for Small samples: t- Test for single mean, difference of means, t-test for correlation coefficients, F- test for ratio of variances, Chi-square test for goodness of fit and independence of attributes. |
10 | 25% |
| 05 | Curve fitting by the numerical method: Curve fitting by of method of least squares, fitting of straight lines, second degree parabola and more general curves. |
04 | 10 % |
Suggested Specification table with Marks (Theory):
| Distribution of Theory Marks |
| R Level | U Level | A Level | N Level | E Level | C Level |
|---|---|---|---|---|---|
| 10% | 10% | 10% | 10% | 10% | row1 col 6 |
Legends: R: Remembrance; U: Understanding; A: Application, N: Analyze and E: Evaluate C: Create and
above Levels (Revised Bloom’s Taxonomy)
Course Outcome:
| Sr. No. | CO statement | Marks % weightage |
|---|---|---|
| CO-1 | understand the terminologies of basic probability, two types of random variables and their probability functions | 20 % |
| CO-1 | observe and analyze the behavior of various discrete and continuous probability distributions | 25 % |
| CO-1 | understand the central tendency, correlation and correlation coefficient and also regression | 20 % |
| CO-1 | apply the statistics for testing the significance of the given large and small sample data by using t- test, F- test and Chi-square test | 25 % |
| CO-1 | understand the fitting of various curves by method of least square | 10 % |
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in this course, the student learns the basic rules of calculating the probabilities and the basics of combinatorics. He or she understands the concept of a random variable and knows the properties of expectation and variance. The student is familiar with the most often used discrete and continuous probability distributions and is able to perform probability calculations under these distributions. The student understands the concept of joint probability distribution and knows the properties of covariance and correlation. The student obtains an understanding how random sampling is used in statistical inference, and why the concept of sample statistic and the distribution of the statistic are important in inference. The student learns the basic principles of estimation and hypothesis testing theory and is able to calculate confidence interval estimates and to perform statistical hypotheses testing especially in situations of one and two groups. The student understands the limitations of the testing theory and is able to calculate different effect size measures.
This course is about uncertainty, measuring and quantifying uncertainty, and making decisions under uncertainty. Loosely speaking, by uncertainty we mean the condition when
results, outcomes, the nearest and remote future are not completely determined; their development depends on a number of factors and just on a pure chance.
Simple examples of uncertainty appear when you buy a lottery ticket, turn a wheel of
fortune, or toss a coin to make a choice.
Uncertainly appears in virtually all areas of Computer Science and Software Engineering.
Installation of software requires uncertain time and often uncertain disk space. A newly
released software contains an uncertain number of defects. When a computer program is
executed, the amount of required memory may be uncertain. When a job is sent to a printer,
it takes uncertain time to print, and there is always a different number of jobs in a queue
ahead of it. Electronic components fail at uncertain times, and the order of their failures
cannot be predicted exactly. Viruses attack a system at unpredictable times and affect an
unpredictable number of files and directories.
Uncertainty surrounds us in everyday life, at home, at work, in business, and in leisure. To
take a snapshot, let us listen to the evening news.
The next chapter introduces a language that we’ll use to describe and quantify uncertainty.
It is a language of Probability. When outcomes are uncertain, one can identify more likely
and less likely ones and assign, respectively, high and low probabilities to them. Probabilities
are numbers between 0 and 1, with 0 being assigned to an impossible event and 1 being the
probability of an event that occurs for sure.
Next, using the introduced language, we shall discuss random variables as quantities that
depend on chance. They assume different values with different probabilities. Due to uncertainty, an exact value of a random variable cannot be computed before this variable is
actually observed or measured. Then, the best way to describe its behavior is to list all its
possible values along with the corresponding probabilities.
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