economist defines the confidence score as 1 if consumer confidence is below 62

Economist defines the confidence score as 1 if

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economist defines the confidence score as 1 if consumer confidence is below 62, 2 if it is between 62 and 65 and 3 if it is above 65. A. According to the economist, what is the probability that the confidence score is 2? X P(X=x) Below 62 1 .35 62-65 2 .4 65+ 3 .25 The probability that the age group is 62-65 will be the complement of the sum of the other 2 probabilities. The probability is .4 B. According to the economist, what is the probability that the confidence score is not 1? This probability is the complement of a score of 1 which is .4 + .25 = .65 or you can do 1- .35 = .65 5.2 14. X 5 10 15 20 P(X=x) 0.35 0.3 0.2 0.15 Mean = E(X) = 5(0.35) + 10(.3) + 15(.2) + 20(.15) = 10.75 Var(X) = 𝜎 2 = 𝛴(x − µ ) 2 P(X = x) = (5 − 10.75 ) 2 (.35) + (10 − 10.75 ) 2 (. 3) + (15 − 10.75 ) 2 (. 2) + (20 − 10.75 ) 2 (.15) = 11.572 + .169 + 3.613 + 12.834 = 28.188 Std(X) = 5.31 16. The number of homes that a realtor sells over a one month period has this distribution. Number of houses sold Probability 0 0.30
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1 0.50 2 0.15 3 0.05 a. On average, how many houses is the Realtor expected to sell over a one month period? E(X) = 0(.3) + 1(.5) + 2(.15) + 3(.05) = 0.95 b. What is the standard deviation? Var(X) = 𝜎 2 = 𝛴(x − µ ) 2 P(X = x) = (0 − 0.95 ) 2 (.3) + (1 − 0.95 ) 2 (.5) + (2 − 0.95 ) 2 (.15) + (3 − 0.95 ) 2 (.05) = .27075 + .00125 + .165375 + .210125 = .6475 Std(X) = .805 5.3 28. What are the portfolio weights for a portfolio that has 100 shares of Stock X that sell for $20 per share and 200 shares of Stock Y that sell for $12 per share?
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