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Let $X$ have gamma distribution with parameters $\alpha=7$ and $\lambda=1$. Investigate the value of $F_X(10)$ using these methods:

  • Find a lower bound using Chebychev's inequality.
  • Approximate the value using the central limit theorem.
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    If this is homework, it should be marked as such. What have you tried so far? Do you know what Chebychev's inequality says? Do you know what the Central Limit Theorem says, and why it is (sort of) applicable in this case?2012-11-30
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    I think I figured out finding the lower bound using Chebychev's inequality. The central limit theorem deals with zn converging with standard normal distribution. I thought I had to calculate zn, which means I need n. I don't understand what the value of n would be.2012-11-30
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    I used the equation z=mean of X-mu/(standard deviation/sqrt(n)) but I'm not sure what n would be.2012-11-30
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    In what way can you think of your Gamma-distributed random variable as a sum of iid random variables?2012-11-30
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    Well, if W_i is the waiting time for the ith arrival, and X is the gamma random variable, X is the sum of w_i with i=1,2,...,7 but I'm still not sure how to use this2012-11-30

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