Problem 9.4.In the compound model for aggregate claims, let the frequency randomvariable N have the geometric distribution with mean 4.Moreover, let the individual losses have the distributionpx (0) = 1/2, px (100) = 1/2.Define the aggregate loss as S=₁X₁. How much is E[(S – 100)+]?

Given that the frequency random variable N follows a geometric distribution with mean 4. The…

Answered: Problem 9.4. In the compound model for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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(4) Annual rainfall over the slopes of southern Himalayan mountains has varied from 750mm to 1250mm over the last several hundred years. If the distribution of the amount of annual rainfall has mean u = 1000mm and standard deviation o = 100mm, what is the likelihood that the average rainfall over the last ten years could have been below 800mm, in the absence of any climate change? Solve this problem by taking the following four steps one by one. Step (i). We need to compute P(X 10 < 800). where X 10 is the average over the ten years of rainfall. Can we compute this probability exactly: (a) No, the population distribution is not known. (b) Yes, since the population distribution is Poisson. (c) Yes, since the population distribution is Binomial. (d) No, because no matter what the population distribution may be, it is always impossible to find the exact distribution of X 10- (e) None of the above. (a) (b) (c) (d) (e) N/A (i- Select One) Step (ii). An approximation to the probability, P(X…
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2
Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. Find a 95% confidence interval for the mean long-term measurement for those with short-term measurements…
Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. A. Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…
15.5 10.5 • 15.5 Suppose f(x)dx = 3, f(x)dx = 10, f(x)dx = 5. 8, 8. 13 f(x)dx 10.5 (3 f(x) – 10)dx = 13
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Problem 9.4. In the compound model for aggregate claims, let the frequency random variable N have the geometric distribution with mean 4. Moreover, let the individual losses have the distribution px (0) = 1/2, px (100) = 1/2. Define the aggregate loss as S = 1 X₁. How much is E[(S-100)+]?