Answer:
A) NO, this is a discrete variable and sum of all probabilities of all outcome (P(X=1)+P(X=2)+P(X=3)=1/6+2/6+3/6=1) is 1. Hence anything other than stated outcome is not possible.
B)
Expected Value E(x)=1*P(X=1)+2*P(X=2)+3*P(X=3)=1/6+4/6+9/6=14/6=2.33
C)
Variance = 1^2*P(X=1)+2^2*P(X=2)+3^2*P(X=3)- E(x)^2=1*1/6+4*2/6+9*3/6-2.333^2=0.556
D) Standard Deviation = =0.7453
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