Answer:
E (X) = 1.8
Var (X) = 0.36
σ = 0.6
Step-by-step explanation:
Solution:-
- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles. 
- Total sample space (bag) have the following quantity of colored marbles:
                 Bag : { 3 Red , 2 Green } 
- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.
- The total number of outcomes / selections for randomly selecting 3 balls from the bag:
                All outcomes = 5 C 3 = 10
- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:
   X = 1 red marble:
         P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.
         P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3
 X = 2 red marble:
         P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.
         P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6
X = 3 red marble:
         P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.
         P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1
- The probability distribution is as follows:
            X :         1                 2                3
        P (X):       0.3            0.6              0.1
- The expected value E(X) for the given random variable X is:
                 E ( X ) = ∑Xi*P(Xi)
                            = 1*0.3 + 2*0.6 + 3*0.1
                            =1.8
- The variance Var(X) for the given random variable X is:
                 Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2
                                = 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2
                                = 0.36
- The standard deviation for the given random variable X is:
                 σ = √Var(X)
                 σ = √0.36
                 σ = 0.6