Q1.Compute the coefficient of skewness by using Karl Pearson and Bowley's method for the following data.

Class 0-2 2-4 4-6 6-8 8-10

frequency 5 18 42 27 8

Q2.The first four moments of a distribution about x =2 are 1, 2.5, 5.5 and 16. Find first four central moment and also find 1 and 2 also give your conclusion about distribution.

Q3.In a distribution, the mean =65, median = 70, coefficient of skewness = - 0.6. Find the mode and coefficient of variation.

Q4.From the following data calculate Karl Pearson's coefficient of skewness.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. of students 4 6 10 20 6 4

Q5.Calculate the Bowley's coefficient of skewness for the following data.

Class interval 0-10 10-20 20-30 30-40 40-50

Frequency 10 14 19 17 13

Q6.If X is random variable denoting the sum obtained in rolling a pair of fair dice, determine its probability mass function.

Q.7Find the distribution function for the random variable x where probability density is given by f(x)=x;for 0

2x;for 1

Q.8A random variable x has the probability density f(x) = 0, x<0

e^-x x>=0

Find the probability for

(i) 1 < x <3 (ii) x> 5 (iii) The distribution function F (x).

Q.9If X is a continuous random variable with the following probability density function

f(x) =a(2x-x²), 0 < x < 2

(i) Find the value of " a". (ii) Find P[X>1].

Q.10A random variable X has the following probability distribution

Values of X 0 1 2 3 4 5 6 7 8

P(x) a 3a 5a 7a 9a 11a 13a 15a 17a

(i)Determine the value of a.

(ii) Find P(x<3); p(X >=3), p (0

(iii)What is the smallest value of x for which

P( X 0.5.

(iv) Also Find E(X).