X is a random variable with mean 8 and variance 16. A function F(X) is defined asF(X) = (2X - 12).Question 7What are the mean and standard deviation of F(X)?Mean 16, standard deviation 32Mean 4, standard deviation 8Mean 4, standard deviation 4Mean 4, standard deviation 16
Question
X is a random variable with mean 8 and variance 16. A function F(X) is defined as F(X) = (2X - 12).
Question 7
What are the mean and standard deviation of F(X)?
- Mean 16, standard deviation 32
- Mean 4, standard deviation 8
- Mean 4, standard deviation 4
- Mean 4, standard deviation 16
Solution
The mean (μ) and variance (σ^2) of a random variable X are given as 8 and 16 respectively.
The function F(X) is defined as F(X) = 2X - 12.
To find the mean of F(X), we substitute X with its mean in the function F(X):
F(μ) = 2*8 - 12 = 16 - 12 = 4
So, the mean of F(X) is 4.
The variance of F(X) is calculated by squaring the coefficient of X in the function F(X) and multiplying it with the variance of X:
σ^2 = (2^2) * 16 = 4 * 16 = 64
The standard deviation is the square root of the variance, so the standard deviation of F(X) is √64 = 8.
Therefore, the mean and standard deviation of F(X) are 4 and 8 respectively. So, the correct answer is "Mean 4, standard deviation 8".
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