For any probability distribution, all probabilities must add up to 1.
From the table:
P(X=0)=0.1
P(X=1)=K
P(X=2)=2K
P(X=3)=2K
P(X=4)=K
Since all probabilities must add up to 1:
P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=1
Substituting the values:
0.1+K+2K+2K+K=1
Combining like terms:
K+2K+2K+K=6K
0.1+6K=1
Solving for K:
6K=1−0.1
6K=0.9
K=60.9
K=0.15
Therefore, the value of K is 0.15.