Final answer:
The variance of the expression 9.2+E+2F, given Var(E)=9 and Var(F)=7 with a Covariance of 2, is calculated as 41 using the formula for the variance of a sum of variables.
Step-by-step explanation:
To calculate Var(9.2+E+2F), we first recognize that the variance of a constant is zero, so the number 9.2 does not affect the variance. Since variance is a measure of spread or dispersion within a set of data, adding or subtracting a constant to all values in a dataset does not change the spread of the data. To calculate the variance of a sum of variables, we utilize the properties that the Variance of the sum of two independent variables is the sum of their variances, and that the Covariance of two variables measures their joint variability.
The formula for the variance of the sum of the variables E and F multiplied by constants is given as:
Var(aX + bY) = a^2 Var(X) + b^2 Var(Y) + 2ab Cov(X,Y),
where a and b are constants, and X and Y are the variables.
Applying the formula to our question, we get:
Var(9.2+E+2F) = Var(E) + 4Var(F) + 2Cov(E, F)
Substituting the given values, we have:
Var(9.2+E+2F) = 9 + 4(7) + 2(2)
Var(9.2+E+2F) = 9 + 28 + 4 = 41
Therefore, the variance of the expression 9.2+E+2F is 41.