Unit 4  Statistical Techniques II, Math 4 Btech AKTU

Unit 4 of Math 4 Btech AKTU is Statistical Techniques II. This section delves into advanced statistical topics such as estimation, hypothesis testing, regression analysis, and analysis of variance. Students will learn how to use statistical software tools such as R and MATLAB to analyze and model data.

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Important Questions For Math 4 (Mathematics 4):
*Unit-01     *Unit-02    
*Unit-03    *Unit-04 
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 

Q1. The students in a class are selected at random, one after the other, for an examination. Find the probability that the boys and girls in the class alternate if 

i. The class consists of 4 boys and 3 girls. 

ii. The class consists of 3 boys and 3 girls.

Ans.

Q2. three urns contain 6 red, 4 black; 4 red, 6 black; 5 red, 5 black balls respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is red find the probability that it is drawn from the first urn

Ans.

Q3. Define a binomial distribution. Prove that the Poisson distribution is the limiting case of binomial distribution. 

Ans. 

Binomial distribution: A random variable x is said to have a binomial distribution ifit assumes only non-negative values and its probability mass function is given by

Q4. Solve this Question

Poisson distribution as a limiting case of binomial distribution: If the parameters n and p of a binomial distribution are known, we can find the distribution. But in situations where n is very large and is very small, application of binomial distribution is very laborious. However,  if we assume that as n >o and p >0 such that np always remains finite, say , we get the Poisson approximation to the binomial distribution. Now, for a binomial distribution 

Ans. 

Q5. Find the mean and variance of binomial distribution

Ans.

Q6. Find the mean and variance of Poisson distribution. 

Ans.

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