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patricehill
14.01.2020 •
Mathematics
Picard partners is planning a major investment. the amount of profit x is uncertain but a probabilistic estimate gives the following distribution (in millions of dollars):
profit 1 1.5 2 4 10
probability 0.1 0.2 0.4 0.2 0.1
a) find the mean profit μxand the standard deviation of the profit.(b) picard partners owes its source of capital a fee of $200,000 plus 10% of the profits x. so the firm actually retains y = 0.9x - 0.2 from the investment. find the mean and standard deviation of y.
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Ответ:
a)
μx=3
σx=2.52
b)
μy=2.5
σy=2.27
Step-by-step explanation:
a)
μx=E(X)=∑x*(p(x))
μx=1*0.1+1.5*0.2+2*0.4+4*0.2+10*0.1=3
μx=3
σx=sqrt(V(x))
σx=sqrt{E(X²)-(E(X))²}
σx=sqrt{(∑x²*(p(x))-(∑x*(p(x)))²}
∑x²*(p(x))=1*0.1+2.25*0.2+4*0.4+16*0.2+100*0.1=15.35
σx=sqrt{15.35-(3)²}=sqrt(6.35)=2.52
σx=2.52
b)
μy=E(Y)=0.9*E(X) - 0.2
μy=0.9*3- 0.2
μy=2.5
σy=sqrt(V(y))
V(y)=0.9²*V(x)-0
V(y)=0.9²*V(x)
V(y)=0.9²*6.35
V(y)=5.14
σy=sqrt(V(y))
σy=sqrt(5.14)
σy=2.27
Ответ:
Explanation is in the file
tinyurl.com/wpazsebu