Calculation of E(2x*^2 3x)

To find the expected value of the given expression, we need to substitute each value of x with its respective probability and then calculate the sum of the products.

Let's substitute the given values of x and their respective probabilities:

E(2x*^2 3x) = (2*(-3)^2*0.1) + (2*(6)^2*?) + (2*(2)^2*0.4) + (2*(1)^2*0.3)

Simplifying the above expression, we get:

E(2x*^2 3x) = (18*?) + (8*0.4) + (2.7)

Now, we need to find the value of '?' that satisfies the equation. To do this, we can use the fact that the sum of probabilities must be equal to 1.

So, we have:

0.1 + ? + 0.4 + 0.3 = 1

Simplifying the above equation, we get:

? = 0.2

Substituting this value of '?' in the expression for E(2x*^2 3x), we get:

E(2x*^2 3x) = (18*0.2) + (8*0.4) + (2.7)

Simplifying the above expression, we get:

E(2x*^2 3x) = 6 + 3.2 + 2.7

Therefore, the expected value of the given expression is:

E(2x*^2 3x) = 11.9