MHB How Do You Calculate the Probability in an Exponential Distribution?

AI Thread Summary
To calculate the probability for a random variable Y with an EXP(2) distribution, the cumulative distribution function (CDF) can be used. The CDF is defined as P[X ≤ x] = 1 - e^(-λx). For P(Y > 1), the calculation involves finding P(Y ≤ 1) first, which is 1 - e^(-2*1), resulting in approximately 0.8467. Consequently, P(Y > 1) is calculated as 1 - 0.8467, yielding a final probability of about 0.1353. This method effectively demonstrates the application of the CDF in determining probabilities in exponential distributions.
das1
Messages
40
Reaction score
0
Help?

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

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

I How to create a fair distribution algorithm?
Replies
1
Views
1K
I Calculating the inverse of a function involving the error function
Replies
3
Views
2K
MHB Continuous joint probability density functions
Replies
3
Views
2K
Finding probability related to Poisson and Exponential Distribution
Replies
6
Views
1K
MHB This is sampling distribution can you help me with this problem
Replies
4
Views
3K
I How to show these random variables are independent?
Replies
1
Views
2K
MHB What is the probability of exceeding maximum weight with a normal distribution?
Replies
2
Views
2K
MHB Win a $10 or $5 Prize in Tom's 4/19 Lottery Fundraiser
Replies
1
Views
2K
MHB Did I Calculate My Funds Distribution Correctly?
Replies
2
Views
1K
MHB Statistics Normal Distribution
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top