Question

Table 1 Column 1 Column 2 Column 3 Profits S1,000s) Project A Probability (% 10 Project B Probability (% S 20 10 40 15 60 50 25 80 40 100 10 10 1.1 Find the expected value, and the standard deviation of X and Y 1.2 Find the distribution functions of Project A (F(x), and Project B (G(x)) 1.3 Find the probability that profits of Project A are less than or equal to $40,000. That is P(XS40) 1.4 Find the probability that profits of Project B are greater than 40,000. That is P(Y>40) 1.5 Consider the random variable Z-X2. Find E(Z) and Variance of Z. 2. Consider a risky prospects that is uniformly distributed: Y U(2, 8) 2.1 Calculate the mean and variance of Y 2.2 Write the equations of the density function and the distribution function of Y 2.3 Find P(Ys5) 2.4 Find P(Y>3) 2.5 Let u(y) - (y)12. Find the expected value of u(y)

Answer 1

Iven Table l Profits PnjeckA 2. 0 Lio 60 80 o1 0 0.15 o 50 o 2 5 b) ツ B · . The Expected value of X(s 10oa Gooo o

2 -360 ฮ LOu 360 0 = 440 ^ .The standard clerianon f ,S ' 1邙20970

o000 65 69 The standard leviabon rf γ ,s 2. where 드 4740-4225

7 22.6336 SD(N)22 69 22-6 22 63 2 lo 2 0 O 10 10 6 o rO

t(ト is given by 0 10 2 0 0.10 60 o.2 5 8o 0-10 13. The Pro bab.hty that. Pnfit Projet A azs less than en eqnal h L40000 15 an veate

2 6 o IS 010 じf

O L 2560000%075ナ129 6съо + 1 ooooooo-16321600