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#   Loesungen Blatt 9    #
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# Aufgabe 1

# 1a)

n = 100
x = rpois( n , lambda=3 )
x
plot(x)
hist(x)


# 1b)

lambda = seq(from = 0.1, to = 10.0, by = 0.1)
lambda


# 1c) 

sumx = sum(x)
sumx

logL = sumx * log(lambda) - n * lambda
logL


# 1d)

plot(lambda, logL)

lambdaML = sumx/n
lambdaML
logL_ML = sumx * log(lambdaML) - n * lambdaML

points( lambdaML , logL_ML , pch = "X", col = "red" )    # ok, das passt..


# pch fuer "plot character"