Formulae/Concepts Needed:
> discrete versus continuous random variables
> notations on discrete random variables
> probability distribution table
> permutation and combination
> probability concepts
Here is the copy of the practice exercises on Discrete Random Variables. The file contains ten (10) items. It contain items with varying difficulty:
You may download the complete copy of the past paper items here (click the image below):
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You may also want to try the previous set of past papers on Past Paper Items on Probability [Part 1] here (click on the image below):
Past Paper Items on Probability [Part 2] here (click on the image below):
Other collection of Cambridge AS/A Level Maths (9709) past papers you might be interested:
Your comments and suggestions are welcome here. Write them in the comment box below. Thank you and God bless!
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ANSWER KEY:
ReplyDelete1)(i)(7C1x3C1)/10C2 = 7/15
(ii) 0 1 2
7/15 7/15 1/15
(iii) E(X) = 3/5
2)(i)P(X=0) = 7C4/10C4 = 1/6
P(X=1) = (7C3x3C1)/10C4 = 1/2
(ii) 0 1 2 3
5/30 15/30 9/30 1/30
(iii) E(X) = 6/5 or 1.2
Var(X)= 14/25 0r 0.56
3)(i) a + b = 0.45
(ii) a = 0.15 and b = 0.3
4)(i) c = 1/18
(ii) E(X) = 25/4 0r 2.78
Var(X)=95/81 or 1.17
(iii) P(X>2.78)= 11/18 or 0.611
5)(i) P(odd) = 2/5
(ii) P(4) = 3/10 or 0.3
(iii) 3 4 5
0.1 0.3 0.6
(iv) E(X) = 4.5
Var(X) = 0.45
6)(i) p = 1/6
(ii) E(X) = 4/3
Var(X) = 68/9 or 7.56
7) p = 0.1
8) 37.5
9)(ii) 120 60 40 30 24 20 120/7 15 40/3
1/45 2/45 3/45 4/45 5/45 6/45 7/48 8/45 9/45
(iii) 40/3 or 13.3
(iv) 4/9 or 0.444
10)(i) p + q = 0.42
-p + 2q = 0.39
p = 0.15 and q = 0.27
(ii) Var(X) = 2.59