problem 1:

a) State and prove the Multiplication theorem of probability.
b) If X, Y are two random variables then prove that E(XY) = E(X). E(Y).

problem 2: Describe the characteristics of the Normal distribution.

problem 3: Describe about Chi square-test and as well prepare the properties of Chi square-test.

problem 4: Fit a second degree polynomial to the given data, taking x as independent variable:

x: 1 2 3 4 5 6 7 8 9
y: 2 6 7 8 10 11 11 10 15

problem 5: Describe about the applications of reliability in the life testing.

problem 6: Assume that 5 men out of 100 and 25 women out of 10,000 are color blind. A color blind person is selected at random. What is the probability of the person being a male? (Suppose male and female to be in equivalent numbers.)

problem 7: Derive the formulae for mean, variance of poisons distribution.

problem 8: If the masses of 300 students are normally distributed with mean 68 kgs and standard deviation 3 kgs. How many students have masses between 65 and 71 kgs inclusive?

problem 9: Derive the relation for the mean of the Normal distribution.

problem 10: In a sample of 64 students have a mean weight of 70 kgs. Can this be regarded as the sample from a population with mean weight 65 kgs and standard deviation 25 kgs.?