IVince Wangol Vince W ango is an up-and-coming artist, who currently has two pai

Question

IVince Wangol Vince W ango is an up-and-coming artist, who currently has two paintings (Starry ight, and Day Caf) exhibited for show and sale at a local art gallery. The curator of the art gallery predicts that there is a 20% chance that both of Wango's paintings will sell, a70% chance that exactly one will sell, and a 10% chance that none of Wango's paintings will sell. Each painting has been priced at $1000. In order to show his work in the exhibition, Wango has agreed to pay the curator $2 regardless of sales outcomes. Let R denote Wango's net earnings from the show; the income from sales minus the fee to the curator. Use this information for Questions 8 to 11 below. 00 in total 8. I1 pt] What are the expected value and standard deviation of the number of paintings Wango will sell? (a) Expected value = 0.900, standard deviation = 0.290 (b) Expected value- 0.900, standard deviation- 0.539 (c) Expected value-1.100, standard deviation = 0.290 (d) Expected value 1.100, standard deviation-0.539 9. I1 pt] What is the expected net earnings, E[R]? (a) $563 (b) $700 (c) $900 (d) $1800 10. I pt) What is the standard deviation of the net earnings, Stdev R]? (a) $339 (b) $395 (c) $539 (d) $739

Explanation / Answer

8)

option D is correct

9)

E(R)=1000*1.1-200=900

10)

Std deviation=0.5385*1000=539

11)

P(R>=1000)=P(X=2)=0.2

x f(x) xP(x) x2P(x) 2 0.2000 0.400 0.800 1 0.7000 0.700 0.700 0 0.1000 0.000 0.000 total 1.100 1.500 E(x) == xP(x) = 1.1000 E(x2) = x2P(x) = 1.5000 Var(x)=2 = E(x2)-(E(x))2= 0.2900 std deviation=         = 2 = 0.5385

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