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Question

Statistics Question on Multivariate Distributions

Let 𝑋1,𝑋2, … be a sequence of 𝑖. 𝑖. 𝑑. random variables such that
P(X1=0)=p(X1=1)=P(X1=2)=13P(X_1=0)=p(X_1=1)=P(X_1=2)=\frac{1}{3}
Let 𝑆𝑛 = 1 𝑛 ∑ 𝑋𝑖 𝑛 𝑖=1 and 𝑇𝑛 = 1 𝑛 ∑ 𝑋𝑖 𝑛 2 𝑖=1 , 𝑛 = 1, 2
Then, the value of 𝛼1+2𝛼2+3𝛼3+4𝛼4 equals

A

6

B

5

C

4

D

3

Answer

6

Explanation

Solution

The correct option is (A): 6