Suppose that Var(X)=2 . The variance of 2−3X is: Var(2−3X)
18
Well, since Var(X) = 2, we know that X has a great personality and an unpredictable nature.
Now, let's calculate the variance of 2 - 3X.
First, the variance of a constant (like 2) is always 0. So, Var(2) = 0.
Next, let's calculate the variance of -3X. Since the variance is a measure of how much a random variable deviates from its expected value, we can say that the variance of -3X is just 3 squared times the variance of X. So, Var(-3X) = 9 * Var(X) = 9 * 2 = 18.
Finally, to find the variance of 2 - 3X, we just add the variances together. So, Var(2 - 3X) = Var(2) + Var(-3X) = 0 + 18 = 18.
So, the variance of 2 - 3X is 18. Just like a clown jumping out of a tiny car, it's unexpected and makes you say, "Wow, that's a lot!"
To find the variance of 2 - 3X, we can use the property that the variance of a constant multiplied by a random variable is equal to the constant squared multiplied by the variance of the random variable.
Let's calculate it step-by-step.
Step 1: Start with the given random variable 2 - 3X.
Step 2: Calculate the constant squared: (-3)^2 = 9.
Step 3: Calculate the variance of X: Var(X) = 2.
Step 4: Multiply the constant squared by the variance of X: 9 * 2 = 18.
Therefore, the variance of 2 - 3X is 18.
To determine the variance of the random variable 2-3X, where Var(X) = 2, we need to use some properties of variance:
1. Var(aX) = a^2 * Var(X) for a constant a.
2. Var(X + c) = Var(X) for a constant c.
We can calculate the variance of 2-3X step by step:
Step 1: Start with the given expression 2-3X.
Step 2: Apply property 1: Var(aX) = a^2 * Var(X)
Var(2-3X) = Var(2 + (-3X))
= Var(2) + Var(-3X)
Step 3: Since Var(2) is the variance of a constant, it is equal to zero.
Var(2-3X) = 0 + Var(-3X)
Step 4: Apply property 1 again:
Var(-3X) = (-3)^2 * Var(X)
= 9 * Var(X)
Step 5: Substitute the given value Var(X) = 2:
Var(-3X) = 9 * 2
= 18
Therefore, the variance of 2-3X is 18.