Math  /  Data & Statistics

Question1. (5.2 MLE) A random sample of size n=9n=9 is taken from the probability function: pY(k;λ)=λk(1λ)1k,k=0,1;0<λ<1p_{Y}(k ; \lambda)=\lambda^{k}(1-\lambda)^{1-k}, k=0,1 ; \quad 0<\lambda<1
The samples are Y1=1,Y2=1,Y3=1,Y4=0,Y5=0,Y6=1,Y7=1,Y8=0,Y9=1Y_{1}=1, Y_{2}=1, Y_{3}=1, Y_{4}=0, Y_{5}=0, Y_{6}=1, Y_{7}=1, Y_{8}=0, Y_{9}=1. Find the maximum likelihood estimate λ^\hat{\lambda} for λ\lambda.

Studdy Solution
Our **maximum likelihood estimate** for λ\lambda is λ^=23\hat{\lambda} = \frac{2}{3}.
So, based on our observations, the best guess for the probability of getting a one is 23\frac{2}{3}!

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