10. Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈...

10. Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈ N(400, 400) and

Z ≈ N(64,64). Let W = X + Y + Z.

a) Describe the distribution of W, give a name and parameters E(W) and Var(W).

b) Use Excel or R to generate 200 random values for X, Y and Z. Add these to obtain 200 values for W. Create a histogram for W. In Excel use the NORMINV(rand(),mean, sd) function.

c) Estimate E(W) and Var(W) using the random numbers.

Expert Solution

milcah answered 7 months ago

Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈ N(400,...

Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈ N(400, 400) and Z ≈ N(64,64). Let W = X + Y + Z. a) Describe the distribution of W, give a name and parameters E(W) and Var(W). b) Use Excel or R to generate 200 random values for X, Y and Z. Add these to obtain 200 values for W. Create a histogram for W. In Excel use the NORMINV(rand(),mean, sd) function. c) Estimate...

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10. Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈...

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