
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 24th, 2017, 01:03 AM  #1 
Newbie Joined: Apr 2017 From: India Posts: 14 Thanks: 0  Exponential Distribution problem
Calls arrive at a switchboard following an exponential distribution with parameter $\lambda$=5 per hour. If we are at the switchboard, what is the probability that the waiting time for a call is 1) at least 15 minutes (Answer: 0.2865) 2)not more than 10 minutes (Answer: 0.6565) 3)exactly 5 minutes (Answer:0){I think this is because the function is a continuous one) My attempt: Firstly formed the Exponential Distribution Function: F(x)= 1  $e^{5x}$ Then for finding the probability : P[X$\ge$15] I am confused at this step. How to approach further? Similarly for second question I am unable to proceed further.For third question , I have given my explanation in the curly brackets above. Please help me out. 
April 24th, 2017, 01:46 AM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,199 Thanks: 611 
if the call rate is exponential the distribution of the number of calls in a period of time is Poisson with the same rate parameter. 1) You want the probability of 0 calls in $\dfrac 1 4~hr$ $P[0] = \dfrac{\left(\frac 5 4\right)^0 e^{\frac 5 4}}{0!} = e^{\frac 5 4} = 0.2865$ you should be able to do (2) and (3) now 
April 27th, 2017, 03:57 AM  #3 
Newbie Joined: Apr 2017 From: India Posts: 14 Thanks: 0 
As per me , answer of second question must be: P [X<10] = 1 P [X>=10] =1  e^(5/6) =0.5654 ( But it is not matching as answer is 0.6565) 
April 27th, 2017, 08:34 AM  #4 
Senior Member Joined: Sep 2015 From: CA Posts: 1,199 Thanks: 611  
April 27th, 2017, 08:50 AM  #5 
Newbie Joined: Apr 2017 From: India Posts: 14 Thanks: 0 
Well, the source I am looking is trustworthy, still there can be mistakes. But why the third answer is zero{(3)exactly 5 minutes}, is it because the distribution function is continuous or is there any other explanation? 
April 27th, 2017, 08:59 AM  #6 
Senior Member Joined: Sep 2015 From: CA Posts: 1,199 Thanks: 611  you are correct about this. the probability of a single point in a continuous distribution is 0.


Tags 
distribution, exponential, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Please help me solve this geometrical & exponential distribution problem  Pcoppus  Advanced Statistics  1  September 13th, 2015 10:57 AM 
Negative exponential distribution to the poisson distribution  alan02011114  Advanced Statistics  0  April 21st, 2015 10:03 AM 
Help in Exponential Distribution  jovic1104  Advanced Statistics  1  July 18th, 2010 01:39 AM 
Simple Exponential distribution problem....need help  rkruz  Algebra  0  July 6th, 2009 10:20 PM 