Solution:

Given, Variance of x = 5

We need to find the variance of (2-3x)

To find the variance of (2-3x), we need to follow the following steps:

Step 1: Find the mean of (2-3x)

Step 2: Find the expected value of (2-3x)

Step 3: Find the variance of (2-3x)

Let's solve the above steps one by one:

Step 1: Find the mean of (2-3x)

Mean of (2-3x) = E(2-3x)

= 2 - 3E(x) [Using linearity of expectation]

= 2 - 3μ [Where μ is the mean of x]

Step 2: Find the expected value of (2-3x)

E[(2-3x) - (2-3μ)]²

= E(-3x + 3μ)²

= 9E(x²) + 9μ² - 18μE(x)

[Using the formula, Var(x) = E(x²) - [E(x)]²]

Step 3: Find the variance of (2-3x)

Variance of (2-3x) = E[(2-3x) - (2-3μ)]²

= 9E(x²) + 9μ² - 18μE(x)

= 9(Var(x) + [E(x)]²) + 9μ² - 18μE(x)

[Using the formula, Var(x) = E(x²) - [E(x)]²]

= 9(5 + μ²) + 9μ² - 18μE(x)

[Substituting Var(x) = 5]

= 45 + 9μ² - 18μE(x) + 9μ²

= 54 + 18(μ² - μE(x))

Therefore, the variance of (2-3x) is 54 + 18(μ² - μE(x)).

Final answer:

Variance of (2-3x) = 54 + 18(μ² - μE(x))