The random variable U has mean 10 and standard deviation 5.The random variable V is de�ned by
V =12(U + 5).Find the mean and standard deviation
of V.
To find the mean and standard deviation of V, we need to use the properties of linear transformations of random variables.
1. Mean of V:
The mean of V can be found by applying the formula for the mean of a linear transformation. In this case, V = 12(U + 5).
We know that the mean of U is 10. To find the mean of V, we substitute the mean of U into the formula:
Mean of V = 12 * (Mean of U + 5)
Mean of V = 12 * (10 + 5)
Mean of V = 12 * 15
Mean of V = 180
Therefore, the mean of V is 180.
2. Standard Deviation of V:
The standard deviation of V can be found using the formula for the standard deviation of a linear transformation.
We know that the standard deviation of U is 5. To find the standard deviation of V, we multiply the standard deviation of U by the constant 12:
Standard Deviation of V = 12 * Standard Deviation of U
Standard Deviation of V = 12 * 5
Standard Deviation of V = 60
Therefore, the standard deviation of V is 60.
To summarize:
Mean of V = 180
Standard Deviation of V = 60