Explanation
To solve for the variance of the transformed variable Y, we use the properties of variance.
1. Determine the Variance of X:
Given that the standard deviation of X is σX=5, the variance is the square of the standard deviation:
Var(X)=(σX)2=52=25
2. Apply the Variance Property for Linear Transformations:
For any constant a and b, the variance of a random variable Y=aX+b is given by the formula:
Var(Y)=a2Var(X)
Note: The constant b does not affect the variance.
3. Calculate the Variance of Y:
In the given equation Y=2X−5, we have a=2.
Var(Y)=22×Var(X)
Var(Y)=4×25
Var(Y)=100
Correct Option:
(d) 100
