X =      1  2  3  4
P(X=x)  0.3 a  b  0.2

From  P(1) + P(2) + P(3) + P(4) = 1,  you have one equation

    0.3 + a + b + 0.2 = 1,

or

    a + b = 0.5.       (1)



From E(X)=2.5, you have another equation

    1*0.3 + 2a + 3b + 4*0.2 = 2.5,

or

    2a + 3b = 1.4.     (2)


Thus you have a system of two equations

     a +  b = 0.5      (1)

    2a + 3b = 1.4      (2)


To solve, multiply equation (1) by 2 (both sides); then subtract from equation (2). You will get then

         3b - 2b = 1.4 - 2*0.5

            b    = 0.4

Then from equation (1)

             a  = 0.5 - 0.4 = 0.1.


ANSWER.  a= 0.1;  b= 0.4.