Question:

Let (𝑋1, 𝑋 ) be a random vector having the probability mass function
𝑓(π‘₯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?

Updated On: Oct 1, 2024
  • 𝐸(𝑋1 + 𝑋2 )=8
  • \(π‘‰π‘Žπ‘Ÿ(𝑋_1 + 𝑋_2 ) =\frac{8}{3}\)
  • \(πΆπ‘œπ‘£(𝑋_1,𝑋_2 ) = βˆ’\frac{5}{9}\)
  • π‘‰π‘Žπ‘Ÿ(𝑋1 + 2𝑋2)=8
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The Correct Option is A, B, D

Solution and Explanation

The correct options are: A, B and D
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