Suppose that on a particular power grid, 30 wind power generating stations each have output which is uniformly distributed between 24 and 36 MW.a) What is the (approximate) probability that the total power available from these 30 stations would exceed 950 MW? Assume that the power generated by each station is independent of other stations (which, of course, doesn’t make much sense, but taking into account dependence needs to know about the covariance between stations, so we’ll ignor that for now).b) What total power level from these 30 stations would have only a 5% chance of being exceeded, approximately?

Suppose that on a particular power grid, 30 wind power generating stations each have output which is uniformly distributed between 24 and 36 MW. a) What is the (approximate) probability that the total power available from these 30 stations would exceed 950 MW? Assume

Suppose that on a particular power grid, 30 wind power generating stations each have output which is uniformly distributed between 24 and 36 MW. a) What is the (approximate) probability that the total power available from these 30 stations would exceed 950 MW? Assume

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

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Question

Suppose that on a particular power grid, 30 wind power generating stations each have output which is uniformly distributed between 24 and 36 MW.
1. a) What is the (approximate) probability that the total power available from these 30 stations would exceed 950 MW? Assume that the power generated by each station is independent of other stations (which, of course, doesn’t make much sense, but taking into account dependence needs to know about the covariance between stations, so we’ll ignor that for now).
2. b) What total power level from these 30 stations would have only a 5% chance of being exceeded, approximately?

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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