Page 341 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes
5 1 ⎡ ⎛⎞ 2 ⎛⎞ 4 ⎤
5
5
= ×⋅ ⎢ + ⎜⎟ + ⎜⎟ + ... ∞ ⎥1
6
6 6 ⎢ ⎝⎠ ⎝⎠ ⎦ ⎥ ⎣
6
⎡ ⎤
51 ⎢ ⎢ 1 ⎥ ⎥ 5 1 36 5
= ×⋅ = ×× =
6 6 ⎢ ⎛⎞ 2 ⎥ 6 6 11 11
5
⎢ − ⎜⎟ ⎥1
⎣ ⎝⎠ ⎦ 6
5
B’s expectation = Rs. 99 × = Rs. 45.
11
Example 18: A bag contains 6 black and 9 white balls. A person draws out 2 balls. If on every black
ball he gets Rs. 20 and on every white ball Rs. 10, find out his expectation.
Solution: There may be the following three options for drawing 2 balls:
(i) Both are white, (ii) Both are black, (iii) One is white and other is black.
(i) Both balls are white
9 C 12
P (2W) = p = 12 C 2 2 = 35

12
Expectation = p × m = × × 10 2 = Rs. 6.86
35
(ii) Both balls are black
6 C 1
P (2B) = p = 15 C 2 = 7
2
1
Expectation = p × m = × × 20 2 = Rs. 5.71
7
(iii) One ball is white and the other is black
6 C × C 18
9
1
P (1W 1B) = p = 15 C 2 1 = 35
18
Expectation = p × m = × ( + )20 10 = Rs. 15.43
35
Total Expectation = 6.86 + 5.71 + 15.43 = Rs. 28
Example 19: If it rains, a taxi driver can earn Rs. 1000 per day. If it is fair, he can lose Rs. 100 per
day. If the probability of rain in 0.4, what is his expectation ?
Solution: The distribution of earnings (X) is given as:

X X = 1000 X = – 100
1 2
P P = 0.4 P = 1 – 0.4 = 0.6
1 2

∴ E (X) = P X + P X
1 1 2 2
= 0.4 × 1000 + 0.6 × (– 100) = Rs. 340
Example 20: A petrol pump dealer sells an average petrol of Rs. 80,000 on a rainy day and an
average of Rs. 95,000 at a clear day. The probability of clear weather is 76% on Tuesday.
What will be the expected sale ?

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