import numpy as np
L = [int(i) for i in input().split()]
N = len(L);M = max(L)
x = list();f = list()
for i in range(M+1):
c=0
for j in range(N):
if L[j]==i:
c = c+1
f.append(c)
x.append(i)
sf = np.sum(f)
p = list()
for i in range(M+1):
p.append(f[i]/sf)
mean = np.inner(x,p)
print(mean)
ex2 = np.inner(np.square(x),p)
var = ex2-mean**2
print(var)
sd = np.sqrt(var)
print(sd)
print("the mean arrival rate is %.3f",mean)
print("the variance of arrival from feeder is %.3f",var)
print("the standard deviation of arrival from feeder is %.3f",sd)

import numpy as np
import math
import scipy.stats
L=[int(i) for i in input().split()]
N=len(L); M=max(L)
X=list();f=list()
for i in range (M+1):
c = 0
for j in range(N):
if L[j]==i:
c=c+1
f.append(c)
X.append(i)
sf=np.sum(f)
p=list()
for i in range(M+1):
p.append(f[i]/sf)
mean=np.inner(X,p)
p=list();E=list();xi=list()
print("X P(X=x) Obs.Fr Exp.Fr xi")
print(" ")
for x in range(M+1):
p.append(math.exp(-mean)*mean**x/math.factorial(x))
E.append(p[x]*sf)
xi.append((f[x]-E[x])**2/E[x])
print("%2.2f %2.3f %4.2f %3.2f %3.2f"%(x,p[x],f[x],E[x],xi[x]))
print(" ")
cal_chi2_sq=np.sum(xi)
print("Calculated value of Chi square is %4.2f"%cal_chi2_sq) table_chi2=scipy.stats.chi2.ppf(1-.01,df=M)
print("Table value of chi square at 1 level is %4.2f"%table_chi2)

import math
import matplotlib.pyplot as plt
import numpy as np
x=[int(i) for i in input().split()]
y =[int(i) for i in input().split()]
N= len(x)
Sx= 0
Sy =0
Sxy =0
Sx2 =0
Sy2 =0
for i in range(0,N):
Sx=Sx+x[i]
Sy=Sy+y[i]
Sxy=Sxy+x[i]*y[i]
Sx2=Sx2+x[i]**2
Sy2=Sy2+y[i]**2
print(Sx)
print(Sy)
print(Sxy)
print(Sx2)
print(Sy2)
r=(N*Sxy-Sx*Sy)/(math.sqrt(N*Sx2-Sx**2)*math.sqrt(N*Sy2-Sy**2))
print("The Correlation coefficient is %0.3f"%r)
byx=(N*Sxy-Sx*Sy)/(N*Sx2-Sx**2)
print(byx)
xmean=Sx/N
ymean=Sy/N
print("THe Regression line Y on X is ::: y = %0.3f + %0.3f
(x-%0.3f)"%(ymean,byx,xmean))
xmean=Sx/N
ymean=Sy/N
print("THe Regression line Y on X is ::: y = %0.3f + %0.3f
(x-%0.3f)"%(ymean,byx,xmean))
plt.scatter(x,y)
def Reg(x):
return ymean + byx*(x-xmean)
x=np.linspace(0,80,51)
y1=Reg(x)
plt.plot(x,y1,'r')
plt.xlabel('x-data')
plt.ylabel('y-data')
plt.legend(['Regression Line','Data points'])

arr_time=float(input("Enter the mean inter arrival time of objects from Feeder (in secs): "))
ser_time=float(input("Enter the mean inter service time of Lathe Machine (insecs) : "))
Robot_time=float(input("Enter the Additional time taken for the Robot (in secs): "))
lam=1/arr_time
mu=1/(ser_time+Robot_time)
print(" -------------------------------------------------------- ")
print("Single Server with Infinite Capacity - (M/M/1):(oo/FIFO)")
print(" -------------------------------------------------------- ")
print("The mean arrival rate per second : %0.2f "%lam)
print("The mean service rate per second : %0.2f "%mu)
if (lam < mu):
Ls=lam/(mu-lam)
Lq=Ls-lam/mu
Ws=Ls/lam
Wq=Lq/lam
print("Average number of objects in the system : %0.2f "%Ls)
print("Average number of objects in the conveyor : %0.2f "%Lq)
print("Average waiting time of an object in the system : %0.2f secs"%Ws)
print("Average waiting time of an object in the conveyor : %0.2f secs"%Wq)
print("Probability that the system is busy : %0.2f "%(lam/mu) )
print("Probability that the system is empty : %0.2f "%(1-lam/mu) )
else:
print("Warning! Objects Over flow will happen in the conveyor")
print(" -------------------------------------------------------- ")

import math
arr_time=float(input("Enter the mean inter arrival time of objects from Feeder (in secs): "))
ser_time=float(input("Enter the mean inter service time of Lathe Machine (insecs) : "))
Robot_time=float(input("Enter the Additional time taken for the Robot (in secs): "))
c=int(input("Number of service centre : "))
lam=1/arr_time
mu=1/(ser_time+Robot_time)
print(" -------------------------------------------------------- ")
print("Multiple Server with Infinite Capacity - (M/M/c):(oo/FIFO)")
print(" -------------------------------------------------------- ")
print("The mean arrival rate per second : %0.2f "%lam)
print("The mean service rate per second : %0.2f "%mu)
rho=lam/(c*mu)
sum=(lam/mu)**c*(1/(1-rho))/math.factorial(c)
for i in range(0,c):
sum=sum+(lam/mu)**i/math.factorial(i)
P0=1/sum
if (rho<1):
Lq=(P0/math.factorial(c))*(1/c)*(lam/mu)**(c+1)/(1-rho)**2
Ls=Lq+lam/mu
Ws=Ls/lam
Wq=Lq/lam
print("Average number of objects in the system : %0.2f "%Ls)
print("Average number of objects in the conveyor : %0.2f "%Lq)
print("Average waiting time of an object in the system : %0.2f secs"%Ws)
print("Average waiting time of an object in the conveyor : %0.2f secs"%Wq)
print("Probability that the system is busy : %0.2f "%(rho))
print("Probability that the system is empty : %0.2f "%(1-rho))
else:
print("Warning! Objects Over flow will happen in the conveyor")
print(" -------------------------------------------------------- ")

arr_time=float(input("Enter the mean inter arrival time of objects from Feeder (in secs): "))
ser_time1=float(input("Enter the mean inter service time of Lathe Machine 1(in secs) : "))
ser_time2=float(input("Enter the mean inter service time of Lathe Machine 2(in secs) : "))
ser_time3=float(input("Enter the mean inter service time of Lathe Machine 3(in secs) : "))
Robot_time=float(input("Enter the Additional time taken for the Robot (in secs): "))
lam=1/arr_time
mu1=1/(ser_time1+Robot_time)
mu2=1/(ser_time2+Robot_time)
mu3=1/(ser_time3+Robot_time)
print(" -------------------------------------------------------- ")
print("Series Queues with infinite capacity- Open Jackson Network")
print(" -------------------------------------------------------- ")
if (lam < mu1) and (lam < mu2) and (lam < mu3):
Ls1=lam/(mu1-lam)
Ls2=lam/(mu2-lam)
Ls3=lam/(mu3-lam)
Ls=Ls1+Ls2+Ls3
Lq1=Ls1-lam/mu1
Lq2=Ls2-lam/mu2
Lq3=Ls3-lam/mu3
Wq1=Lq1/lam
Wq2=Lq2/lam
Wq3=Lq3/lam
Ws=Ls/(3*lam)
print("Average number of objects in the system S1 : %0.2f "%Ls1)
print("Average number of objects in the system S2 : %0.2f "%Ls2)
print("Average number of objects in the system S3 : %0.2f "%Ls3)
print("Average number of objects in the overall system : %0.2f "%Ls)
print("Average number of objects in the conveyor S1 : %0.2f "%Lq1)
print("Average number of objects in the conveyor S2 : %0.2f "%Lq2)
print("Average number of objects in the conveyor S3 : %0.2f "%Lq3)
print("Average waiting time of an object in the conveyor S1 : %0.2f secs"%Wq1)
print("Average waiting time of an object in the conveyor S2 : %0.2f secs"%Wq2)
print("Average waiting time of an object in the conveyor S3 : %0.2f secs"%Wq3)
else:
print("Warning! Objects Over flow will happen in the conveyor")
print(" -------------------------------------------------------- ")