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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.

Respuesta :

Answer:

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

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