Suppose that X is a random variable with mean = 10 and standard deviation = 3....
Suppose that X is a random variable with mean = 10 and standard deviation = 3. Suppose that Y is a random variable with mean = 20 and standard deviation = 4. Suppose that X and Y are independent. Find the standard deviation of X+Y.
| A. |
5 |
|
| B. |
7 |
|
| C. |
3.5 |
|
| D. |
25 |
Homework Answers
The variance of X+Y is given by,
Var(X+Y) = Var(X) + Var(Y) +2Cov(X,Y)
Since , X and Y are independent.
Therefore , Cov(X,Y) = 0
Therefore ,
Var(X+Y) = Var(X) + Var(Y) +2Cov(X,Y) = 32 + 42 + 2*0 = 25
The standard deviation of X+Y is 
=
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