0
1
2
3
Answer is Right!
Answer is Wrong!
The correct answer is $\boxed{\text{B}}$.
The variance of a random variable is a measure of its spread. It is calculated by taking the square of the standard deviation. The standard deviation is a measure of how far the values of the random variable are from the mean.
The variance of a sum of two independent random variables is the sum of their variances. This is because the values of the sum are just the sum of the values of the two random variables, so the spread of the sum is just the sum of the spreads of the two random variables.
In this case, $X$ and $Y$ are two independent random variables with variances 1 and 2, respectively. So, the variance of $Z = X – Y$ is $1 + 2 = \boxed{3}$.
Here is a more detailed explanation of each option:
- Option A: 0. This is the variance of a constant random variable. A constant random variable always takes the same value, so its spread is 0. However, $X$ and $Y$ are not constant random variables, so this cannot be the answer.
- Option B: 1. This is the variance of a random variable with mean 0. The mean of a random variable is the average of its values. If a random variable has mean 0, then its values are all equally likely to be positive or negative. This means that the spread of the random variable is equal to its standard deviation, which is 1. However, $X$ and $Y$ do not have mean 0, so this cannot be the answer.
- Option C: 2. This is the variance of a random variable with mean 1. The variance of a random variable is equal to the square of its standard deviation. The standard deviation of a random variable with mean 1 is 1, so the variance is 2. However, $X$ and $Y$ do not have mean 1, so this cannot be the answer.
- Option D: 3. This is the correct answer. As explained above, the variance of a sum of two independent random variables is the sum of their variances. In this case, $X$ and $Y$ are two independent random variables with variances 1 and 2, respectively. So, the variance of $Z = X – Y$ is $1 + 2 = \boxed{3}$.