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only 3 question of probability of normal continuous distributions. please step by step. all the requirement are on the pdf.
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MTH 34200 – HW 06 (20 points) – Due Tuesday, 10/9
Name_______________________________________
̂1 be an estimator for a parameter 𝜃. Assume that 𝐸[𝜃
̂1 ] = 𝑘𝜃 and Var[𝜃
̂1 ] = 𝑐𝜃 2.
3. (10 pts) Let 𝜃
̂1 ] in terms of 𝜃, 𝑐, and 𝑘.
a) Find 𝐵[𝜃
Bias=sum of variance/no of periods
̂1 ] = ⅀𝑐𝜃 2 /( 𝐸[𝜃
̂1 ] = 𝑘𝜃)
Bias=sum of Var[𝜃
= ⅀𝑐𝜃 2 / 𝑘𝜃
̂1 ] in terms of 𝜃, 𝑐, and 𝑘.
b) Find 𝑀𝑆𝐸[𝜃
MSE=Sum of Variance/n-1
̂1 ] − 1 = 𝑘𝜃-1)
𝑀𝑆𝐸 = ⅀𝑐𝜃 2/( 𝐸[𝜃
= ⅀𝑐𝜃 2 /( 𝑘𝜃-1)
̂2 for 𝜃. Define 𝜃
̂2 as a function of of 𝜃
̂1 .
c) Define a new unbiased estimator 𝜃
̂2 =( 𝑘𝜃
̂1 + 1)/𝑘𝜃
̂1
𝜃
̂2 ] in terms of 𝜃, 𝑐, and 𝑘.
d) Find Var[𝜃
̂2 ] = 𝑐𝜃 2 *(k 𝜃) /(k �...