Example:Buffon's Needle We model (X,)with a uniform joint PDF so that 4 fre到midc3 otherwiseExample: Buffon’s Needle ◼ We model (𝑋, 𝜗) with a uniform joint PDF so that 𝑓𝑋,𝜗 𝑥, 𝜃 = ൞ 4 𝜋𝑑 , 𝑖𝑓 𝑥 ∈ 0, 𝑑 2 𝑎𝑛𝑑 𝜃 ∈ [0, 𝜋 2 ] 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒