How Do You Calculate the Probability in an Exponential Distribution?

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Discussion Overview

The discussion revolves around calculating the probability in an exponential distribution, specifically for a random variable Y with an EXP(2) distribution. Participants explore the use of cumulative distribution functions (CDF) and probability density functions (pdf) in this context.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks for help calculating P(Y > 1) for Y ~ EXP(2).
  • Another participant questions whether to use the CDF or pdf for the calculation.
  • Some participants assert there are no restrictions on the functions that can be used for the calculation.
  • A participant provides the CDF formula for the exponential distribution and suggests using it to find the probability.
  • There is a calculation proposed where one participant suggests plugging in values into the CDF to find P(Y > 1) and arrives at a numerical answer.
  • A later reply confirms the calculation appears correct.

Areas of Agreement / Disagreement

There is no explicit consensus on the preferred method for calculating the probability, as some participants discuss using the CDF while others mention the pdf. The discussion remains somewhat unresolved regarding the best approach.

Contextual Notes

Participants do not clarify any assumptions regarding the use of CDF versus pdf, and there are no explicit restrictions mentioned on the methods used for calculation.

Who May Find This Useful

This discussion may be useful for students or individuals learning about probability distributions, particularly the exponential distribution, and those seeking to understand different methods of calculating probabilities within this context.

das1
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Help?

Suppose the random variable Y has an EXP(2) distribution. What is P(Y > 1)? (Round to four decimal places as appropriate.)
 
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das said:
Help?

Suppose the random variable Y has an EXP(2) distribution. What is P(Y > 1)? (Round to four decimal places as appropriate.)

Are you allowed to use the CDF for this distribution or should you calculate this purely from the pdf? Either way you'll need to also use this fact: $$P[Y>2]=1-P[Y \le 2]$$
 
I don't think there are any restrictions on what functions I can or can't use
 
das said:
I don't think there are any restrictions on what functions I can or can't use

Ok, then this should be very useful. For the exponential distribution, the CDF is the following: $$P[X \le x]=1-e^{-\lambda x}$$. How can you use this to answer your question?
 
So would I plug in 1 for x and 2 for λ?
Then we would get 1-e^(-2*1)? Which is .8467 but we'd actually want 1-.8467 again because we're looking for P(Y > 1) right? So about .1353?
 
That looks good to me! (Yes)
 

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