GIVEN THE FOLLOWING STATISTICAL VARIABLES A:m(A)=5 B:m(B)=13
var(A)=25 Var(B)=6
1.calculate mean of Z= 4B-2A
2.Calculate the Standard Deviation assuming cov (A,B)=0
To calculate the mean of Z=4B-2A, we can use the given values of m(A) and m(B).
1. Mean of Z:
First, we calculate the mean of 4B and 2A separately.
- Mean of 4B = 4 * m(B) = 4 * 13 = 52
- Mean of 2A = 2 * m(A) = 2 * 5 = 10
Next, we subtract the mean of 2A from the mean of 4B.
- Mean of Z = Mean of (4B - 2A) = 52 - 10 = 42
Therefore, the mean of Z is 42.
To calculate the standard deviation assuming Cov(A,B) = 0, we need to consider the variances of A and B.
2. Standard Deviation:
Since Cov(A,B) = 0, we can assume that A and B are independent. Therefore, the variance of the sum or difference of two independent variables is the sum of their variances.
- Variance of Z = Variance of (4B - 2A)
= (4^2 * Var(B)) + (2^2 * Var(A))
= (16 * 6) + (4 * 25)
= 96 + 100
= 196
Taking the square root of the variance gives us the standard deviation.
- Standard Deviation of Z = Square Root of Variance of Z = √196 = 14
Therefore, assuming Cov(A,B) = 0, the standard deviation of Z is 14.