Given:

a.m of x = 10

coefficient of variation of x = 40

y = 15 - 2x


Calculating Variance:

To calculate the variance of y, we need to find the variance of x first. Let's use the formula:

coefficient of variation = (standard deviation / mean) * 100

standard deviation = (coefficient of variation / 100) * mean

standard deviation of x = (40/100) * 10 = 4



Now we can use the formula to calculate the variance of y:

variance of y = variance of (15 - 2x)

variance of y = variance of 15 - variance of 2x (since variance is a linear operator)

variance of y = 0 - 4^2 * variance of x (since variance of a constant is 0)

variance of y = -16 * 16 = -256


Explanation:

The coefficient of variation is a measure of relative variability. It is the ratio of the standard deviation to the mean, expressed as a percentage. In this case, the coefficient of variation of x is 40%, which means that the standard deviation of x is 4 (since 40% of 10 is 4).



To calculate the variance of y, we need to use the formula for the variance of a linear function of a random variable. The variance of a linear function of a random variable is equal to the square of the coefficient of the random variable times the variance of the random variable. In this case, the coefficient of x is -2, so the square of the coefficient is 4. The variance of x is 16 (since the standard deviation is 4), so the variance of y is -256 (since -16 * 16 = -256).



Note that the variance of y is negative, which means that the distribution of y is not well-defined. This is because the function y = 15 - 2x is a linear function of x, which means that the variance of y depends entirely on the variance of x. If the variance of x is too large, then the variance of y will be negative, which means that the distribution of y is not well-defined.

AMx=10 , COVx=40, 15-2x
AMy=5,
COVy=100×SDy/AMy
80=SDy×100/5
SDy=4
Vy=2