The mean and SD for a, b and 2 are 3 and 2/√3 respectively, the value of ab would be?

Question

Answer

Calculation of ab given mean and SD of a, b and 2

To calculate the value of ab, we need to use the formula:

SD_ab = √[(SD_a)²(b)² + (SD_b)²(a)² + 2(a)(b)(Cov_ab)]

where SD_a, SD_b, Cov_ab are the standard deviations and covariance of a and b respectively.

Finding the covariance of a and b

Since we do not have the covariance of a and b, we need to estimate it using the formula:

Cov_ab = [E(ab) - E(a)E(b)]

where E(ab), E(a), and E(b) are the expected values of ab, a, and b respectively.

Finding the expected values of a, b, and ab

Since we have the mean of a, b, and 2, we can find the expected values of a and b as follows:

E(a) = 3

E(b) = 3

E(2) = 2

Now, we need to find the expected value of ab:

E(ab) = E(a)E(b) + Cov_ab

Finding the standard deviations of a, b, and ab

Now that we have the expected values of a, b, and ab, we can find the standard deviations of a, b, and ab as follows:

SD_a = 2/√3

SD_b = 2/√3

SD_ab = √[(SD_a)²(b)² + (SD_b)²(a)² + 2(a)(b)(Cov_ab)]

Calculating the value of ab

Now that we have all the necessary values, we can calculate the value of ab as follows:

ab = (E(ab) - E(a)E(b))/Cov_ab

Substituting the values we get:

ab = (9 - 9)/Cov_ab

ab = 0/Cov_ab

ab = 0

Conclusion

Therefore, the value of ab is 0 given the mean and SD of a, b, and 2 are 3 and 2/√3 respectively.