please solve: In the table below x denotes the Z-Lab Company\'s projected annual
ID: 1179073 • Letter: P
Question
please solve:
In the table below x denotes the Z-Lab Company's projected annual profit (in $1,000), along with the probability of earning that profit. The negative value indicates a loss. The probability that Z-Lab will break even is, f(x = 0) = . 0.05 0.10 0.15 0.20 The probability that Z-Lab will be profitable, that is, f(x > 0) = . 0.20 0.95 0.90 0.80 The mean or expected value of Z-Lab's profit is mu = E(x) = . $103 thousand $111 thousand $117 thousand $121 thousand The variance of profit is var(x) = 6,211.00 5,568.75 5,125.30 4,500.45 On average, each profit (loss) amounts deviate from the mean profit by thousand. 71.59 74.62 78.81 81.84 Suppose $100 thousand is added to each previously projected profit (loss) level (y = 100 + x), but probabilities are maintained as before. The updated expected value of profit and the variance of profit for Z-Lab, respectively, are: Suppose, instead of adding $100 thousand, each profit (and loss) amount is doubled (y = 2x) and probabilities maintained as before. The new expected value of profit and the variance of profit for Z- Lab, respectively, are:Explanation / Answer
3) sum of probabilities is equal to 1.
0.05 + x + 0.25 + 0.40 + 0.1 + 0.05 = 1
x = 1 - 0.85 = 0.15 option c is answer.
4) f(x>0 = 0.25+0.4+0.1+0.05 = 0.8 option d is answer.
5) mean = -100*0.05 + 0*0.15 + 80*0.25 + 140*0.4+200*0.1+240*0.05 = $103 thousand
option a is answer.
6) varaince = E(x^2) - (E(x))^2 =
10000*0.05 + 0*0.15 + 6400*0.25 + 140*140*0.4+200*200*0.1+240*240*0.05 - 103^2
= 6211
option a is answer.
7) standard deviation = sqrt( 6211) = 78.809897855535887 = 78.81 option c is answer.
8) y = 100+x
E(y) = E(100+ x) = 100 +E(x) = 100 + 103 = 203
variance = E(y^2) - E(y))^2 = E(100+x)^2 - E(y)^2
= E(10000+200x+x^2) - 203^2
= 10000 + 200E(x) + E(x^2) -203^2
= 10000 + 200*103 + 6211+103^2 - 203^2
= 6211
option a is answer.
9) y = 2x
E(y) = E(2x) = 2E(x) = 2*103 = 206
varaince = var(2x) = 4Var(x) = 4*6211 = 24844
option c is answer.
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