Let X₁, X₂, X₃, ..., Xₙ be a random sample of size n taken from an exponential distribution with unknown parameter β. Find the likelihood function for the unknown parameter.

L(β) = n ln(β) − ∑
i=1
n
​
xᵢ − ln(β)

L(β) = β⁻ⁿ e^(β) − ∑
i=1
n
​
xᵢ

L(β) = βⁿᵉ e^(β) − Π
i=1
n
​
xᵢ

L(β) = ∑
i=1
n
​
β⁽¹⁄ⁿ⁾ e^(β⁽¹⁄ⁿ⁾) − ∑
i=1
n
​
xᵢ
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