P&S ASSIGNMENT-1

PS ASSIGNMENTG QUESTIONS

1. Find the mean, variance, mode median of the normal distribution.

2. Find the mean, variance, mode, recurrence relation for

a. Binomial

b. Poisson distribution

3. The probability that john hits a target is ½. He fires 6 times. Find the probability that he hits the target

i) exactly 2 times

ii) atleast 2 times

iii) atmost 2 times

iv) more than 4 times

v) atleast once

4. Fit a binomial distribution to the following data:

x	0	1	2	3	4	5	6
f	13	25	52	58	32	16	4

5. State and prove Baye’s theorem. Do 1 problem on it/

6. P.T if E₁, E₂, E₃ are random events in a sample space and if E₁, E₂, E₃ are pair wise independent and E₁ is independent of E₂ U E₃ then E₁, E₂, and E₃ are mutually independent.

7. The students in a class are selected at random one after the other for an examination. Find the probability that the boys and girls in the class are arranged alternately if

i) The class consists of 4 boys and 3 girls

ii) 3 boys and 3 girls

8. Define the following:

i) Binomial Experiment

ii) Equally likely events

iii) Exhaustive events

iv) Probability

v) Conditional event

vi) Conditional prabability