returns on a certain business venture, to the nearest $1,000, are known to follow the following probability distribution x p(x) -2,000 0.1 -1,000 0.1 0 0.2 1000 0.2 2000 0.3 3000 0.1 (i) what is the most likely monetary outcome of the business venture? (ii) is the venture likely to be successful? explain (iii) what is the long-term average earning of business ventures of this kind? explain
Answers
Given : Returns on a certain business venture, to the nearest $1,000, are known to follow the following probability distribution
X P(x)
-2,000 0.1
-1,000 0.1
0 0.2
1000 0.2
2000 0.3
3000 0.1
To Find : most likely monetary outcome of the business venture
is the venture likely to be successful
what is the long-term average earning of business ventures of this kind
Solution:
most likely monetary outcome of the business venture is 2000 $
as it has maximum probability = 0.3
E(X) P(x) E(X)P(X)
-2,000 0.1 -200
-1,000 0.1 -100
0 0.2 0
1000 0.2 200
2000 0.3 600
3000 0.1 300
800
Expected value = ∑E(X)P(X) = 800
long-term average earning of business ventures = 800 $
venture is likely to be successful as Expected value is + ve = 800 $
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