Question
If the random variable X has mean 3 and standard deviation 5, then what is the variance of the random variable Y=2X-5 ?
NDA
Mathematics
Statistics
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 15
- B. 40
- C. 45
- D. 100
Answer
D. 100
Step-by-step solution
Given the standard deviation of X is 5. The variance of X is Var(X) = 5^2 = 25. Using the property of variance, Var(aX + b) = a^2 Var(X). For the random variable Y = 2X - 5, we have a = 2 and b = -5. Var(Y) = 2^2 Var(X) = 4 25 = 100. Answer: 100
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