Tom K. answered 11/14/20
Knowledgeable and Friendly Math and Statistics Tutor
P(X =0) = (1/10)^2 + (2/10)^2+(3/10)^2 + (4/10)^2 = 30/100 = 3/10
P(X = 1) = 2*(1/10*2/10+2/10*3/10+3/10*4/10) = 40/100 = 2/5
P(X = 2) = 2*(1/10*3/10+2/10*4/10) = 22/100 = 11/50
P(X = 3) = 2 * 1/10 * 4/10 = 8/100 = 2/25
As a check, notice that 3/10 + 4/10 + 11/50 + 2/25 = 1