Probability and Statistics for Data Science (AD-302) - Important Questions

Define Data Science. Explain the Data Science life cycle with its different phases.

Calculate the mean and standard deviation for the following grouped frequency distribution of age of 542 members.

The first four moments of a distribution about the value 5 are 2, 20, 40 and 50. Calculate the first four central moments about the mean and hence find beta1 and beta2 and comment on skewness and kurtosis.

In a bolt factory, machines A, B and C manufacture respectively 25%, 35% and 40% of the total. Of their output 5%, 4% and 2% are defective bolts. A bolt is drawn at random and found to be defective. Using Bayes' theorem find the probability that it was manufactured by machine A, B or C.

Fit a second-degree parabola y = a + bx + cx^2 by the method of least squares to the given (x,y) data.

Derive the mean and variance of the Binomial distribution.

Calculate Karl Pearson's coefficient of correlation between two variables X and Y from the given bivariate data.

Obtain the Spearman's rank correlation coefficient between variables X and Y from the given data.

A machine set to turn out washers of thickness 10 mils. A sample of 10 washers has an average thickness of 9.52 mils with a standard deviation. Test whether the mean thickness differs significantly from 10 mils using single-sample t-test at 5% level.

Test the hypothesis about a single normal population variance sigma = 10 using chi-square test given sample standard deviation s = 15 for a random sample of size 50 from a normal population.

A manufacturer knows that the condensers he makes contain on an average 1% defectives. He packs them in boxes of 100. Using Poisson distribution, find the probability that a box picked at random will contain 4 or more faulty condensers.

Ten coins are thrown simultaneously. Find the probability of getting at least seven heads.

Fit a straight line y = a + bx by the method of least squares to the given (x,y) data and find the least-square linear trend.

Given X follows Normal distribution N(mu, sigma^2) with mean 100 ohms and standard deviation 2 ohms, find P(X >= a) and P(a < X < b), i.e. percentage of resistors with resistance between 98 and 102 ohms.

For a distribution, Bowley's coefficient of skewness is -0.56, Q1 = 16.4 and Median = 24.2. Find the coefficient of quartile deviation.

From the given discrete bivariate (x,y) data, determine the two lines of regression of Y on X and X on Y.