if V(X)=3 then find
1)V(X+10)
2)V(X-3)
3)V(5X)
4)V(2X+3)
Substitute 3 for x and solve, e.g.:
1)V(X+10) = 13
To find the variance of a random variable, you can use some basic properties of variance:
1) V(X + a):
When you add a constant value (a) to a random variable (X), the variance remains the same. So, V(X + a) = V(X) = 3.
2) V(X - b):
Similarly, when you subtract a constant value (b) from a random variable (X), the variance remains unchanged. So, V(X - b) = V(X) = 3.
3) V(cX):
If you multiply a random variable (X) by a constant value (c), the variance gets multiplied by the square of that constant. Therefore, V(cX) = c^2 * V(X).
For V(5X), since c = 5, we have:
V(5X) = (5^2) * V(X) = 25 * 3 = 75.
4) V(aX + b):
When you apply a linear transformation to a random variable (X), the variance gets multiplied by the square of the coefficient multiplying X. So, for V(aX + b), we have:
V(aX + b) = (a^2) * V(X).
For V(2X + 3), a = 2, so we have:
V(2X + 3) = (2^2) * V(X) = 4 * 3 = 12.
Therefore, the answers are:
1) V(X + 10) = V(X) = 3.
2) V(X - 3) = V(X) = 3.
3) V(5X) = 75.
4) V(2X + 3) = 12.