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Statistics

Notes 1.8 Review Questions

1. Classify the experiments described below as random or non-random experiments.
(a) A spark of electricity is introduced in a cylinder containing a mixture of hydrogen
and oxygen. The end product is observed.
(b) A lake contains two types of fish. Ten fish are caught and the number of fish of each
type is noted.

(c) The time taken by a powerful radio impulse to travel from the earth to the moon
and for its echo to return to the sender is observed.
(d) Two cards are drawn from a well-shuffled pack of 52 playing cards and the suits
(Club, Diamond, Heart and Spade) to which they belong are noted.
2. Write down the sample spaces of all those experiments from 3 to 11 which we have not
discussed earlier. Indicate in each case the assumptions made by you.
3. Let A , A , A and A be arbitrary events. Find expressions for the events that correspond
1 2 3 4
to occurrence of
(a) only A and A ,
1 2
(b) none of A , A , A and A ,
1 2 3 4
(c) one and only one of A , A , A , A ,
1 2 3 4
(d) not more than one of A , A , A , A
1 2 3 4
(e) at least two of A , A , A , A .
1 2 3 4
4. Express in words the following events:
c
(a) A  A  A 3
2
1
c
c
c
c
c
(b) (A  A  A )  (A  A  A )
1
2
3
1
2
3
(c) (A  A ) – (A  A )
1 2 3 4
(d) (A  A )  A
1 2 3
(e) (A  A )  (A  A )  (A  A )
1 2 2 3 3 1
Answers: Self Assessment
1. (b) 2. (a) 3. (b) 4. (c) 5. (d) 6. (d)
1.9 Further Readings
Books Introductory Probability and Statistical Applications by P.L. Meyer
Introduction to Mathematical Statistics by Hogg and Craig
Fundamentals of Mathematical Statistics by S.C. Gupta and V.K. Kapoor

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