How Do You Calculate the Probability in an Exponential Distribution?

[das1]

Help?

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

 

[Jameson]

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: $$P[Y>2]=1-P[Y \le 2]$$

 

[das1]

I don't think there are any restrictions on what functions I can or can't use

 

[Jameson]

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?

 

[das1]

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?

 

[Jameson]

That looks good to me! (Yes)