The mean and standard deviation (SD) of two variables, a and b, are given as 2 and 2/√3, respectively. We need to determine the value of the product ab. Let's break down the problem step by step.

Step 1: Understanding Mean and Standard Deviation
Mean is a measure of central tendency that represents the average value of a set of numbers. Standard deviation measures the dispersion or spread of the data points around the mean. It provides information about how much the individual data points deviate from the mean.

Step 2: Calculating Variance
To find the product of a and b, we first need to calculate the variance of each variable. Variance is the square of the standard deviation.

The variance of a is equal to the square of its standard deviation:
Variance of a = (Standard deviation of a)^2
= (2)^2
= 4

The variance of b is equal to the square of its standard deviation:
Variance of b = (Standard deviation of b)^2
= (2/√3)^2
= (4/3)

Step 3: Understanding Covariance
To find the product ab, we need to understand the concept of covariance. Covariance is a measure of how much two variables change together. It gives us information about the relationship between two variables.

Step 4: Calculating Covariance
The covariance of a and b is given by the formula:
Covariance(a, b) = (Variance of ab) - (Mean of a * Mean of b)

Step 5: Finding the Value of Covariance
Since the mean of a and b are given as 2, the covariance of a and b can be calculated as:
Covariance(a, b) = (Variance of ab) - (2 * 2)

We know that the variance of a is 4, and the variance of b is 4/3. Therefore, we can rewrite the equation as:
Covariance(a, b) = (Variance of ab) - 4

Step 6: Solving for Variance of ab
Rearranging the equation, we get:
(Variance of ab) = Covariance(a, b) + 4

Step 7: Determining the Value of ab
To find the value of ab, we need to calculate the variance of ab first. Then, we can substitute the value of variance of ab into the equation:
ab = (Variance of ab) + 4

Step 8: Substitute Values and Calculate
Using the given mean and standard deviation, we substitute the values into the equation and solve for ab:
ab = (Covariance(a, b) + 4) + 4
ab = Covariance(a, b) + 8

Step 9: Final Answer
Since the covariance value is not provided in the given information, we cannot calculate the exact value of ab. However, we have derived the equation ab = Covariance(a, b) + 8, which gives us a general formula to calculate the product of a and b once the covariance value is known.

Therefore, the value of ab depends on the covariance between variables