interarrival times in exponential distributions
Arrivals occur following a Poisson distribution with a rate parameter of 84 arrivals per hour. Find: the probability that the time to arrival of the next customer is less than one minute.
When calculating the interarrival rate, would I have to convert it into minutes as the question is asking for the probability that is is less than an minute but the rate parameter has been given in terms of hours.
If this is the case, would the interarrival rate be 1/84 per hour; then converting into minutes would make it 0.714 minutes
See also questions close to this topic

Exponentional function parameters
I have 3 points
[x0 y0]
,[x1 y1]
,[x2 y2]
with strict conditionalx0<x1<x2
,y0<y1<y2
. All this points lay on some exponentional functionsy=ae^(bx)+c
. I need to finda,b,c
... It's not possible to solve system of 3 equations precisely, therefore I need to approximate it. Is there some math library in java that will help me solve this problem? I find something similar on mathcadhttps://help.ptc.com/mathcad/en/index.html#page/PTC_Mathcad_Help/exponential_regression.html but not find in java.
Other way  how to solve system of 3 equations and 3 values approximately.
ae^(bx_0)+c=y_0 ae^(bx_1)+c=y_1 ae^(bx_2)+c=y_2

MATLAB Exponential (exp2) curve fitting function not giving the same output as the plot graph when using the fit values in the original equation
my brain is pickled with this one. Below are the two graphs I have plotted with exp2 function. The points do not match the curve, and this is ultimately changing my entire answer, as it is giving the wrong values out, and I cannot understand why? enter image description here enter image description here
Here is the code I am using, both graphs plot a concentration against time, but yet give different results:
CH4_fit = fit(Res_time, CH4_exp, 'exp2'); CH4_coeff = coeffvalues(CH4_fit);
%Coefficient values for exponential fitting CH4_pred =(CH4_coeff(1)*exp(CH4_coeff(2)*Res_time)) + ... (CH4_coeff(3)*exp(CH4_coeff(4)*Res_time)); plot(Res_time,CH4_exp, Res_time, CH4_pred);Can I just added that the exact same data was run on different computers, and it gave the same equation coefficients exactly (to 4.dp) and the same times, but yet still outputs different concentrations on my version? I have the R2018b, and I have just used default settings (don't know how to change anything, so I definitely haven't).

Count entries based on exponential notation values with pure awk
I am trying to count the entries that are less than the e threshold of 1e5 in my tabdel data file that looks something like the table below.
col1 col2 col3 eval
entry1   1e10
entry2   
entry3   0.001
I used this code:
$: awk F"\t" '{print $4}' table.txt  awk '($1 + 0) < 1e5'  grep [09*]  wc l
This outputs:
$: 1
While this works, I would like to improve the command into something pure awk. I would love to know how to do this in awk. Also, I would like to know how to print the line that satisfies the threshold if this is possible. Thank for helping!

Ageadjusted rate to fit GLM Poisson in R
I have a rate between the years 2005 and 2016:
years < c(2005:2016) count < c(20535, 20526, 19694, 18452, 17402, 16551, 15679, 14691, 13409, 13378, 12772, 12417) #cases pop< c(68435380, 69295253, 70158111, 71051678, 72039206, 73142150, 74223628, 75175826, 76147624, 77181884, 78218478, 79277962) #population
Fitting the crude rate to GLM Poisson is:
glm(count~years+offset(log(pop)), family=poisson)
It is OK for me but how about calculating ageadjusted rate and then to fit GLM Poisson in R? My variables of the same data:
years < c(2005:2016) agecat < c("04", "514", "1524", "2534", "3544", "4554", "5564", "65+") weight < c(5, 11, 11.5, 12.5, 14, 14, 12.5, 19.5) #european standart population countcat_2005 < c(293, 942, 4962, 4461, 3201, 2831, 1886, 1959) #agecategorized count of the cases in 2005 popcat_2005 < c(5979662, 12665031, 12679110, 11546527, 9426447, 7104654, 4432038, 4601908) #agecategorized population in 2005
Agecategorized counts and population of the other years could also be provided.
Thank you.

KolmogorvSmirnov Test in R package(dgof) Discrete Case
I have the following data,
Data < c(8, 15, 8, 10, 7, 5, 2, 11, 8, 7, 6, 6, 4, 6, 10, 3, 9, 7, 15, 6, 5, 9, 8, 3, 3, 8, 5, 14, 8, 11, 8, 10, 7, 4, 6, 4, 6, 7, 11, 7, 8, 7, 8, 6, 5, 12, 7, 8, 13, 10, 6, 9, 7)
and I want to perform a KS test in R using the
dgof
package but have no idea how to use it. I also fit the above data with binomial and Poisson distribution.Now, I want to use KS test to identify which model (binomial or Poisson) represents the data.
Thank you.

Homogeneous Poisson Point Processes
I'm plotting homogeneous spatial Poisson processes on various types of plots. I cannot figure out how to plot only on the upper right triangular area of the rectangular area. I added a polygon to the graph to define where I want to plot, but do not know how to restrict the points to all only plot on the top half of the rectangle.
N=50 u=runif(N,20,40) v=runif(N,10,10) plot(u,v,asp=1) polygon(c(0,0,55.5),c(10,11.5,10),col=NA,border='black')
Currently, I get this graph:
How do I get all the points to the top triangle??