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Statistics Question on Limit Theorems

Let (𝑋1, 𝑋 ) be a random vector having the probability mass function
𝑓π‘₯1, π‘₯2 = { 𝑐 π‘₯1! π‘₯2! 12 βˆ’ π‘₯1 βˆ’ π‘₯2 ! , if π‘₯1, π‘₯2 ∈ {
where 𝑐 is a real constant. Then, which of the following statements is/are TRUE?

A

𝐸(𝑋1 + 𝑋2 )=8

B

π‘‰π‘Žπ‘Ÿ(𝑋1+𝑋2)=83π‘‰π‘Žπ‘Ÿ(𝑋_1 + 𝑋_2 ) =\frac{8}{3}

C

πΆπ‘œπ‘£(𝑋1,𝑋2)=βˆ’59πΆπ‘œπ‘£(𝑋_1,𝑋_2 ) = βˆ’\frac{5}{9}

D

π‘‰π‘Žπ‘Ÿ(𝑋1 + 2𝑋2)=8

Answer

𝐸(𝑋1 + 𝑋2 )=8

Explanation

Solution

The correct options are: A, B and D