1.
A random variable X has a mean of 10 and a standard deviation of 3. A random variable Y has a mean of 15 and a standard deviation of 4. What is the mean of the combined random variable X + Y?
2.
A random variable X has a mean of 10 and a standard deviation of 3. A random variable Y has a mean of 15 and a standard deviation of 4. What is the standard deviation of the combined random variable X + Y?
A random variable X has a mean of 10 and a standard deviation of 3. A random variable Y has a mean of 15 and a standard deviation of 4. What is the mean of the combined random variable X + Y?
2.
A random variable X has a mean of 10 and a standard deviation of 3. A random variable Y has a mean of 15 and a standard deviation of 4. What is the standard deviation of the combined random variable X + Y?
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1. You add the means. So the mean is 10 + 15 = 25
2. This answer depends on whether X and Y are independent. (Or to be more precise "uncorrelated", but I'm trying to keep it simple). I think they intend you to assume that they are independent of each other, but it was a mistake on the part of your teacher/prof to not state this. Anyway, if you assume independence, you add the variances:
Var(X + Y) = Var(X) + Var(Y)
Variance is standard deviation squared, so
Var(X) = 3^2 = 9
Var(Y) = 4^2 = 16
=> Var(X+Y) = 25
=> standard deviation of X+Y = square root of 25 = 5
2. This answer depends on whether X and Y are independent. (Or to be more precise "uncorrelated", but I'm trying to keep it simple). I think they intend you to assume that they are independent of each other, but it was a mistake on the part of your teacher/prof to not state this. Anyway, if you assume independence, you add the variances:
Var(X + Y) = Var(X) + Var(Y)
Variance is standard deviation squared, so
Var(X) = 3^2 = 9
Var(Y) = 4^2 = 16
=> Var(X+Y) = 25
=> standard deviation of X+Y = square root of 25 = 5