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If the random variable X has mean 3 and standard deviation 5 , then what is the variance of the random variable Y=2X-5 ?

Options

  1. A15
  2. B40
  3. C45
  4. D100

Correct 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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