X^4-6x^3+17x^2-28x+20

The expected value of X, E(X), for the given probability distribution is 1.2

Step-by-step explanation:

Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E(x).

Hope is the sum of the product of the probability of each event and the value of that event. That is, it is the sum of the probability of each possible event multiplied by the frequency of said process, this indicates that if you have a discrete quantitative variable X with "n" possible events x₁, x₂, x₃... xₙ and probabilities P (X = xi) = Pi the mathematical expectation is:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + ... + xₙ*Pₙ

In this case:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + x₄*P₄

Being:

and replacing:

E(x)= 0* 0.5 + 1* 0.1 + 2*0.1 + 3*0.3

you get:

E(x)= 1.2

The expected value of X, E(X), for the given probability distribution is 1.2