0 votes 0 votes Suppose avg waiting time of a process to get chance in a queue is 5 min. What will the probability that process get chance at first minute is ________________ Probability probability + – srestha asked Feb 19, 2019 srestha 1.7k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 2 votes 2 votes For the detailed solution , please see the pic below SuvasishDutta answered Jun 30, 2019 • selected Jun 30, 2019 by srestha SuvasishDutta comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments SuvasishDutta commented Aug 2, 2019 reply Follow Share @srestha mam, please see the pic below for the answer. Here the lifetime of the product is 0<T<3 T>=2 states that the product will work fine till 2 or more years i.e it includes 0<T<=2 and 2<T<3 and T>=3. But as the product breaks down in 3rd year, we have to remove T>=3 from above. Thus the required probability is P(T>=2) - P(T>=3). 1 votes 1 votes srestha commented Aug 3, 2019 reply Follow Share Probability will be $\frac{e^{-\frac{2}{4}}-e^{-\frac{3}{4}}}{e^{-\frac{2}{4}}}$ right?? i.e. $P\left ( A/B \right )=\frac{P\left ( A\cap B \right )}{P\left ( B \right )}$ 0 votes 0 votes SuvasishDutta commented Aug 3, 2019 reply Follow Share No. Required probability= P(0<T<3) = P(T>=2)-P(T>=3) I had given the explanation. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes Avg waiting time $\lambda$ = $5$ min. average rate is $1$ process in $5$ minutes i.e. $1/5$ According to exponential distribution, $P(X<=1) = \int_{0}^{1}\frac{1}{5}e^{-\frac{t}{5}}dt = 1- e^{-\frac{1}{5}} = 1- 0.81=0.18$ Satbir answered Jun 28, 2019 • edited Jun 30, 2019 by Satbir Satbir comment Share Follow See all 24 Comments See all 24 24 Comments reply srestha commented Jun 29, 2019 reply Follow Share I think it will be $e^{-{5}}$ chk it https://courses.lumenlearning.com/introstats1/chapter/the-exponential-distribution/ 0 votes 0 votes Satbir commented Jun 29, 2019 reply Follow Share But in every question it is mentioned that it is exponentially distributed. Also in the link check the relation between exponential and poisson distribution. 0 votes 0 votes srestha commented Jun 29, 2019 reply Follow Share with exponential distribution, how much do u get? 0 votes 0 votes Satbir commented Jun 29, 2019 reply Follow Share average rate is 1 process in 5 minutes i.e. 1/5 P(X<=1) = $\int_{0}^{1}\frac{1}{5}e^{-\frac{t}{5}}dt = 1- e^{-\frac{1}{5}} = 1- 0.81=0.18$ 0 votes 0 votes srestha commented Jun 29, 2019 reply Follow Share Here we need to find $P\left ( X=1 \right )$, less than sign not required. What will be $\mu ?$ Is it $5$ or $\frac{1}{5}?$ Here exponential distribution is more appropriate than poisson distribution. right? 0 votes 0 votes Satbir commented Jun 29, 2019 reply Follow Share why we don't need to find before 1st minute ? at first minute means from 0 to 60 sec right ? we will just calculate pdf not cdf ? mean will be 1/ $\lambda$ = 5. Yes exponential will be more appropriate. 0 votes 0 votes srestha commented Jun 29, 2019 reply Follow Share @Satbir but why r u converting it in second? Everything is minute here 0 votes 0 votes Satbir commented Jun 29, 2019 reply Follow Share I am using minute only. Just want to say that it is continous and not discrete thats why we need to use cdf and not pdf right ? 0 votes 0 votes srestha commented Jun 29, 2019 reply Follow Share where do u got pdf is discrete case? 0 votes 0 votes srestha commented Jun 29, 2019 reply Follow Share Another point, why exponential better here? 0 votes 0 votes Satbir commented Jun 30, 2019 reply Follow Share CDF is cumulative so it will include past values also right ? but Pdf will only calculate at P(x=1) i.e at a particular point. In the question probability of waiting time is asked. The waiting times for poisson distribution is an exponential distribution with parameter lambda. https://stats.stackexchange.com/questions/2092/relationship-between-poisson-and-exponential-distribution Read the 2nd last answer. 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share Execution of process starts from t=0 or 0th time instant( here minute ). In the question it is mentioned to find the probability that the process gets chance to execute at the first minute i.e. t=1. If the question says average service time then exponential distribution should be used. If the question says numbers of events occured or arrived at a given time period, then poisson distribution is used. 1 votes 1 votes Satbir commented Jun 30, 2019 reply Follow Share @SuvasishDutta So here we will use poisson or exponential ? and PDF will be used or CDF ? 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share Here we will use exponential distribution. Between cdf and pdf which one to use is shown in the pic below. In the pic, it is explained that if we use either cdf or pdf the value will remain unchanged. Hence for this question any of them can be used. 1 votes 1 votes Satbir commented Jun 30, 2019 reply Follow Share So it doesn't matter whether the given values we take them as discrete values or continous values ? 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share No it matters. In the previous comment i am saying that the value of cdf and pdf or value of cdf and pmf are same. Discrete or continuous values depends on what distribution we use. 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share I have provided an answer to the question. Please check. 0 votes 0 votes Satbir commented Jun 30, 2019 reply Follow Share So, the conclusion is first we see what distribution to use by looking whether we have to calculate it for discrete values or continous and other things like what is asked in question. then we can either calculate its pdf or cdf 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share Absolutely perfect @Satbir . 1 votes 1 votes srestha commented Jun 30, 2019 reply Follow Share @Satbir pdf and cdf both can take continuous value 0 votes 0 votes Satbir commented Jun 30, 2019 reply Follow Share okay 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share @srestha mam, pdf can take only continuous values, pmf can take only discrete values, but cdf can take both discrete and continuous values. For continuous probability distribution, c.d.f take continuous values i.e. a range of values. For discrete probability distribution, c.d.f take discrete values. 1 votes 1 votes srestha commented Jun 30, 2019 reply Follow Share @SuvasishDutta yes, right. By the way, from where u read for this probability portion, like exponential, pmf, pdf, cdf portion? 0 votes 0 votes SuvasishDutta commented Jun 30, 2019 reply Follow Share From grewal book and made easy engg maths book 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes By Using the poisson distribution and substituting the average rate to 3, Probality is 0.149 Rakshit Aaryan answered Feb 20, 2019 Rakshit Aaryan comment Share Follow See 1 comment See all 1 1 comment reply srestha commented Jun 28, 2019 i reshown by srestha Jul 1, 2019 reply Follow Share not clear 0 votes 0 votes Please log in or register to add a comment.