How do I find the distribution of years until X1 is exceeded for the first time?

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SUMMARY

The discussion focuses on deriving the distribution of years until the first occurrence of sunny days, represented by the random variable X1, is exceeded. Participants suggest starting with the Poisson distribution as a potential method for solving this problem. The conversation emphasizes the importance of showing work and understanding the underlying concepts rather than seeking direct answers. The need for a solid grasp of probability theory and statistical distributions is highlighted as essential for tackling this question effectively.

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  • Understanding of continuous random variables
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  • Knowledge of the Poisson distribution
  • Basic principles of statistical independence
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baoheli
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Hello all, I have a question about distribution. Can you help me? Thank you!

Here is the problem:

X1,X2,... are continuous and independent, with marginal pdf f(x). Xi represents the of sunny day of the ith year. How to derive the distribution of the number of years until the first year's sunny days, X1, is exceeded for the first time?
 
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This looks like homework to me. Either way, you need to show some working or point out what you struggle with. No one is going to hand a solution to you.
 

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