Worksheet: Variance of Two Independent Discrete Random Variables

In this worksheet, we will practice calculating the variance of two independent discrete random variables.

Q1:

Suppose 𝑋 and 𝑌 are independent, V a r ( 𝑋 ) = 2 4 , and V a r ( 𝑌 ) = 3 0 . Determine V a r ( 7 𝑋 + 9 𝑌 ) .

Q2:

Suppose 𝑋 and 𝑌 are independent, V a r ( 𝑋 ) = 4 , and V a r ( 𝑌 ) = 1 8 . Determine V a r ( 3 𝑋 + 5 𝑌 ) .

Q3:

Suppose 𝑋 and 𝑌 are independent, V a r ( 𝑋 ) = 9 , and V a r ( 𝑌 ) = 3 6 . Determine V a r ( 5 𝑋 + 8 𝑌 ) .

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