# Inference Statistic - Likelihood Function

#### StefanGray

##### New Member
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Can anyone help me understand this?

Consider the four observations from de Normal Distribution with variance equal to one $y_1 < 10$$, y_2 > 10$, $5 < y_3 < 10$ and $y_4 = 10$.
The likelihood function is?

Would be:

$\prod_{1}^{4} \frac{1}{\sqrt(2\pi)}\exp{-\frac{(y_i - \theta )^2}{2}}$

Replacing:

$(\int_{-\infty }^{10}\frac{1}{\sqrt(2\pi)}\exp{-\frac{(y_1 - \theta )^2}{2} dy}) \cdot (\int_{10 }^{\infty}\frac{1}{\sqrt(2\pi)}\exp{-\frac{(y_2 - \theta )^2}{2} dy})\cdot (\int_{5}^{10}\frac{1}{\sqrt(2\pi)}\exp{-\frac{(y_3 - \theta )^2}{2}}dy)\cdot (\frac{1}{\sqrt(2\pi)}\exp{-\frac{(10 - \theta )^2}{2}})$

I want to know if this is correct or have another way of solving this problem.