The mean and SD for a, b and 2 are 3 and 2/root 3 respectively. find the value of ab. pls do show the steps?

Question

Answer

Answer

Answer

Answer

Given:

Mean of a, b, and 2 = 3

Standard deviation of a, b, and 2 = 2/√3

To Find:

Value of ab

Solution:

Let’s assume the data follows a normal distribution.

Step 1: Finding the Variance
Variance of a set of data can be calculated using the formula:

Variance = (Standard Deviation)^2

Variance of a, b, and 2 = (2/√3)^2 = 4/3

Step 2: Forming Equations
We know that the sum of a, b, and 2 is 3. Therefore, we can form two equations as follows:

a + b + 2 = 3 ---(1)
ab = (a + b + 2 - 3)(3 - 2) = (a + b - 1) ---(2)

Step 3: Solving Equations
We can substitute equation (1) in equation (2) and get:

ab = (a + b - 1) = (3 - 2 - 2) = -1

Now, we can substitute the value of ab in equation (1) and get:

a + b + 2 = 3
a + b = 1

Squaring both sides, we get:

(a + b)^2 = 1
a^2 + b^2 + 2ab = 1
Since ab = -1, we can substitute the value and simplify:

a^2 + b^2 - 2 = 1
a^2 + b^2 = 3

Step 4: Solving for a and b
We can solve the above two equations to find the values of a and b:

a + b = 1
a^2 + b^2 = 3

Substituting a = 1 - b in the second equation, we get:

(1 - b)^2 + b^2 = 3
2b^2 - 2b - 2 = 0
b^2 - b - 1 = 0

Solving the quadratic equation, we get:

b = (1 ± √5)/2
a = 1 - b

Therefore, the two possible sets of values for a and b are (a,b) = (-0.618, 1.618) and (a,b) = (1.618, -0.618).

Step 5: Finding the Value of ab
We can substitute the values of a and b in equation (2) and get:

ab = (a + b - 1) = (1.618 + (-0.618) - 1) = -1

Therefore, the value of ab is -1.

Answer:

The value of ab is -1.

Answer

Mis printed
SD = square root of 14/3
answer= 6
a and b= 1 and 6

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