In
a reality show, two judges independently provided marks base do the performance
of the participants. If the marks provided by the second judge are given by Y =
10.5 + 2x, where X is the marks provided by the first judge. If the variance of
the marks provided by the second judge is 100, then the variance of the marks provided
by the first judge is:
🎥 Video solution / Text Solution of this question is given below:
Statistics Puzzle: Variance under Linear Transformation
Given:
Y = 10.5 + 2X
Var(Y) = 100
Formula: If Y = a + bX, then Var(Y) = b² × Var(X)
Apply:
100 = 2² × Var(X)
100 = 4 × Var(X)
Var(X) = 100 / 4 = 25
✅ Final Answer:The variance of the marks given by the first judge is 25.