If ๐‘‹X and ๐‘ŒY are independent random variables with ๐ธ[๐‘‹]=1E[X]=1, Var(๐‘‹)=2Var(X)=2, ๐ธ[๐‘Œ]=3E[Y]=3, and Var(๐‘Œ)Var(Y) = 4, then find ๐ธ[(2๐‘‹+3๐‘Œ)2]E[(2X+3Y) 2 ].

Question

If ๐‘‹X and ๐‘ŒY are independent random variables with ๐ธ[๐‘‹]=1E[X]=1, Var(๐‘‹)=2Var(X)=2, ๐ธ[๐‘Œ]=3E[Y]=3, and Var(๐‘Œ)Var(Y) = 4, then find ๐ธ[(2๐‘‹+3๐‘Œ)2]E[(2X+3Y) 2 ].
๐Ÿง Not the exact question you are looking for?Go ask a question

Solution 1

To find E[(2X+3Y)^2], we first need to expand the square. This gives us:

E[(2X+3Y)^2] = E[4X^2 + 12XY + 9Y^2]

Since X and Y are independent, E[XY] = E[X]E[Y]. We can substitute this into the equation:

E[(2X+3Y)^2] = E[4X^2] + E[12XY] + E[9Y^2] = 4E[X^2] + 12E[X]E[Y] + 9E[Y^2]

We kn Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

If ๐‘‹X and ๐‘ŒY are independent random variables with ๐ธ[๐‘‹]=1E[X]=1, Var(๐‘‹)=2Var(X)=2, ๐ธ[๐‘Œ]=3E[Y]=3, and Var(๐‘Œ)Var(Y) = 4, then find ๐ธ[(2๐‘‹+3๐‘Œ)2]E[(2X+3Y) 2 ].

G) For two random variables ๐‘‹ and ๐‘Œ, ๐ธ(๐‘‹๐‘Œ) = ๐ธ(๐‘‹)๐ธ(๐‘Œ) hold if ๐‘‹ and ๐‘Œ are _______

Equation of a Straight LineWhat would be the equation of the given line?Y = X/2 + 3Y = 2X + 3Y = X/3 + ยฝY = 3X + ยฝ

Find the solution of the system of equations.minus, 2, x, minus, 3, y, equals, minus, 28โˆ’2xโˆ’3y=โˆ’28minus, 2, x, plus, 2, y, equals, 22โˆ’2x+2y=22

Solve the following logarithmic equations: (Criteria A)a) log4(2x+1)=2b) 3log(xโˆ’2)=6c) 4ln(2x+3)=4d) log3(x+1)โˆ’log3(2xโˆ’1)=1e) 2loga(3x+1)=loga(9)

1/3