An insurance company selected 6000 drivers from a city at random in order to find a relationship between age and accidents. The following table shows the results to these 6000 drivers.

 If a driver from the city is selected at random, find the probability of the following events:
a) Age lying between 18 – 25 and meet 3 accidents
b) Age lying between 18 – 40 and meet 1 accident
c) Age more than 25 years and meet at most one accident
d) Having no accident in the year
e) Age lying between 18 – 40 and meet at least 3 accidents

Which of the following statements are true or false? Give reason in support of your answer.
a) When two dice are thrown simultaneously then total number of sample points in the sample space will be 12.
b) Expected value of a continuous random variable X is defined as
E(X) =x f (x)dx
c) If X and Y are independent random variable then V(X – Y) = V(X) – V (Y).
d) If X ~ B(4,3) then variance of X is 12.
e) If probability density function of a normally distributed random variable X is
, - ∞ <x< ∞
then variance of X is 36.

600 candidates were appeared in an examination. The boys outnumbered girls by 15% of all candidates. Number of passed exceeded the number of failed candidates by 300. Boys failing in the examination numbered 80. Determine the coefficient of association.

Board of Directors of Labour Union wishes to sample the opinion of its members before submitting a change in its contribution at a forthcoming annual meeting. Questionnaires are sent to a random sample of 200 members in three union locals. The results of the survey are as follows:

Determine the amount of association between the Union locals and their reactions using coefficient of contingency and interpret the result.

Calculate the first, second and third quartile for the following data:

Also find the quartile deviation and coefficient of quartile deviation.

Fit an exponential curve of the form Y = abX to the following data:

A statistician wanted to compare two methods A and B of teaching. He selected a random sample of 22 students. He grouped them into 11 pairs so that the students in pair have approximately equal scores on an intelligence test. In each pair one student was taught by method A and the other by method B and examined after the course. The marks obtained by both methods are given as:

Find the rank correlation coefficient.

If a, b, c, d are constants, then show that the coefficient of correlation between ax+b and cy+d is numerically equal to that between x and y.

A researcher collects the following information for two variables x and y:
 n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, σ_x = 4 and σ_y = 5
 Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y).

The equations of two regression lines are given as follows:
4x – 5y + 30 = 0
20x−9y – 107 = 0
Calculate

(i) regression coefficients, byx and bxy;

(ii) correlation coefficient r(x, y);

(iii) Mean of X and Y; and

(iv) the value of σ_y if σ_x = 3

Mean and Standard deviation of 18 observations are found to be 7 and 4, respectively. On comparing the original data, it was found that an observation 12 was miscopied as 21 in the calculations. Calculate correct mean and standard deviation.

The frequency distribution of the marks obtained by the 25 students each of the two sections is given as follows:

Find which section is more consistent.

If AM and GM of two numbers are 30 and 18, respectively, find the numbers.

Find the missing information from the following data:

State whether the following statements are True or False and also give the reason in support of your answer.
a) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
b) Mean deviation is least when calculated from the median.
c) The correlation coefficient between x and (a – x) is –1.
d) The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
e) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.

Draw a histogram for the following data:

Also draw frequency polygon in the same graph.

Find the values of a and b, if the function f given below is continuous at x = 2

Draw a box plot with whisker, +ve sign and outliers for the following data: 42, 37, 28, 23, 32, 25, 26, 39, 38, 41, 22, 38, 21, 31, 26, 36, 42, 52, 50, 47, 24, 53, 28

What do you mean by primary data and secondary data? Also give an example in each case

Prove that  = (a+b+c)(ab+bc+ca-a²-b²-c²)