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Suppose X is a random variable with a mean of 10 and a variance of 100. Suppose Y is a random variable with a mean of 2 and a standard deviation of 16. Also, suppose X and Y are independent. What is the mean of 10 X + 3 Y?

Respuesta :

MrRoyal

Answer:

[tex]E(10x + 3y) =106[/tex]

Step-by-step explanation:

Given

[tex]E(x) =10[/tex]

[tex]Var(x) = 100[/tex]

[tex]E(y) =2[/tex]

[tex]Var(y) = 16[/tex]

Required

[tex]E(10x + 3y)[/tex]

To do this, we make use of the following equation

[tex]E(ax + by) =aE(x) + bE(y)[/tex]

So, we have:

[tex]E(10x + 3y) =10 * E(x) + 3 *E(y)[/tex]

[tex]E(10x + 3y) =10 * 10 + 3 *2[/tex]

[tex]E(10x + 3y) =100 + 6[/tex]

[tex]E(10x + 3y) =106[/tex]

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