Define statistics and discuss its importance in the field of computational sciences. The following are the numbers of minutes that a person had to wait for the bus to work on 20 working days : 15, 10, 2, 17, 5, 8, 3, 10, 2, 9, 5, 9, 13, 1, 10, 12, 5, 10, 8, 4. Compute mean, median, mode, standard, variance and coefficient of variation.

Define normal distribution. What are the main chracteristics of normal distribution? Extruded plastic rods are automatically cut into length 5 inches. Actul length are normally distributed about a mean of  5 inches and their standard deviation is 0.05 inches. (i) What propotion of rods exceed tolerance limits of 4.9 inches to 5.1 inches? (ii) Proportion of rods having tolerance rod which is greater than 6.5 inches.

Diffrence between correlation and regression analysis. Raw materials are used in the production od synthesis and fiber are stored in a place which has no humidity control. Measurement of relative humidity in the storage place and the moisture content of a sampleof a raw materials (both in percentage) on 10 days yeilds the following results.

1. Compute correlation coefficiet between humidity and moisture content and interpret the result.
2. Find the regression equation of moisture content on humudity.
3. Estimate the moisture content if humudity is 45%
4. Interpreat the value of regression coefficient.

What is sampling? Explain the main purpose of sampling. Describe briefly stratified sampling.

What do you understand by measurement of dispersion? Two batsman A and B made the following runs in a series of cricket matches.

Who is more consistent player? Give your statistical reasoning.

Define skewness and kurtosis. The first four moments about mean are 0, 14.75, 39.75 and 152.31. Compute skewness and kurtosis and interprete the results.

What are partition values? From the following distributionof scores 200 students of a college :

Compute (i) the minimum scores obtained by top 10% students (ii) the range of middle 60 % students.

Define mutually exclusive events and independent events in probability. A problem of mathematics is given to three students, A, B and C whose chances of solving the problem are in ratio 2 : 3 : 5. Find the probability that (i) all of them solve the problem. (ii) none of them solve the problem. (iii) the problem will be solved.

Define Baye’s theorem. Store A, B and C have 100, 75 and 50 employees and, respectively 70, 60 and 50 percent of these are women. Registration are equally likely among all employees regardless of sex. One employee resigns, and this is woman. What is the probability that she works in store B?

Under what condition binomial probability distribution. Five unbaised coins are tossed 100 times and the following results were obtained.

Fit the binomial distribution.

Define poission probability distribution. Cars arrive at a petrol station at an average rate of 3 per minute. Assuming that the cars arrive at random, find the probability that (a) no cars arrive during a particular minute. (b) at least one car arrive during a particular minute (c) four cars arriving per 2 minutes.

Let X and Y be two continuous random variable having joint pdf
f(x,y) = c(x² + y²), 0< x <1, 0< y<1
= 0 , otherwise.

Determine (a) the value of c. (b) P(x < 0.5,  y > 0.5).

Write short notes on any two:

1. Random variable and probability distribution
2. Five number summary
3. Sampling error.