Could someone here maybe explain the answer to this question, and how you got that answer?
Before planting a crop for the next year, a producer does a risk assessment. According to her assessment, she concludes that there are three possible net outcomes: a $7,000 gain, a $4,000 gain, or a $10,000 loss with probabilities 0.55, 0.20, and 0.25, respectively.
What is the variance and standard deviation of the random variable?
Before planting a crop for the next year, a producer does a risk assessment. According to her assessment, she concludes that there are three possible net outcomes: a $7,000 gain, a $4,000 gain, or a $10,000 loss with probabilities 0.55, 0.20, and 0.25, respectively.
What is the variance and standard deviation of the random variable?
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Variance = E(X^2) - [E(X)]^2
Where E(X^2) = SUM of x^2 * P(x) for all x, and similarly E(X) = SUM of x * P(x) for all x
x = the gain or loss outcomes
P(x) = the probability of that outcome
E(X) = 0.55*7000 + 0.2*4000+0.25*-10000 = 2150
E(X^2) = 0.55*7000^2+0.2*4000^2+0.25*(-10000^2) = 55,150,000
Variance = 55,150,000 - (2150^2) = 50,527,500
Standard deviation is the square root of variance or = 7108.269
Alternative method:
Variance = SUM of P(x)*(x-mean)^2
= 0.55(7000-2150)^2+0.2*(4000-2150)^2+0.25…
Where E(X^2) = SUM of x^2 * P(x) for all x, and similarly E(X) = SUM of x * P(x) for all x
x = the gain or loss outcomes
P(x) = the probability of that outcome
E(X) = 0.55*7000 + 0.2*4000+0.25*-10000 = 2150
E(X^2) = 0.55*7000^2+0.2*4000^2+0.25*(-10000^2) = 55,150,000
Variance = 55,150,000 - (2150^2) = 50,527,500
Standard deviation is the square root of variance or = 7108.269
Alternative method:
Variance = SUM of P(x)*(x-mean)^2
= 0.55(7000-2150)^2+0.2*(4000-2150)^2+0.25…