JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II STATISTICAL METHODS FOR DATA SCIENCE Previous Question Paper (August/September - 2022 - R18)

A coin is tossed until a head appears. Expect the number of tosses required?

Let X be a random variable with the density function

Explain Binomial distribution. Derive its moment generating function and hence find its mean and variance.

Suppose the weights of 500 male students are normally distributed with mean = 150 with a standard deviation of 15. Find the number of students whose weights are between 140 and 165.

The joint distribution of X and Y is given by

If the random variable X takes the values 1, 2, 3 and 4 such that 2P(X=1) = 3P(X=2) = P(X=3) = 5P(X=4), derive the probability distribution function and cumulative distribution function of X.

The joint probability density function is given by

The joint probability density function of the random variables is given by

Fit a Poisson distribution to the following data and test for the goodness of fit: X: 0, 1, 2, 3; Frequency: 24, 15, 6, 5.

A sample of 100 electric bulbs produced by manufacturer A showed a mean lifetime of 1190 hours and a standard deviation of 90 hours. A sample of 75 bulbs produced by manufacturer B showed a mean lifetime of 1230 hours, with a standard deviation of 120 hours. Is there a difference between the mean life time of two brands at a significance level of 0.05?

In a sample of 1000 students 500 use ball pen and in another sample of 3500 students 1400 use ball pens. Test the significance between the differences of two proportions at 5% level.

A random sample of 400 items is found to have mean 82 and standard deviation 18. Find the maximum error of estimation at 95% confidence interval and the confidence limits for the mean if mean is 82.

Eleven school boys were given a test in drawing. They were given a month's further tuition and a second test of equal difficulty was held at the end of it. Do the marks give evidence that the students have benefitted by extra coaching? (Data: Boys 1-11; Marks I test: 23, 20, 19, 21, 18, 20, 18, 17, 23, 16, 19; Marks II test: 24, 19, 22, 18, 20, 22, 20, 20, 23, 20, 17)

Two random samples are drawn from two populations: Sample I (16, 17, 18, 19, 20, 21, 22, 23, 24) and Sample II (12, 17, 18, 22, 27, 23, 32). Find the variances of the two samples and test whether the two populations have the same variance at 5% level of significance.