Suppose X is a discrete random variable and k is a constant. If E(3X+k)=26 and E(2k-X)=3 , what is E(X)?

1 Answer
Jan 29, 2016

E(X)=7

Explanation:

The calculation is nearly similar to substitution equation except for this time, you used density function as its equation.

For a discrete random variable X, where a and b are constant, the equation is given as;

E [ a X +- b ] = a E(X) +- b

So, in order to find E(X) you need to rearrange the equations, which can be seen as;

E(3X+k)=26
3E(X)+k=26 ----- (1)

E(2k-X)=3
-E(X)+2k=3 ----- (2)

Then, to solve for E(X), we can use substitution equation;

From (1);
3E(X)+k=26
k=26-3E(X) ----- (3)

Substitute (3) into (2);
-E(X)+2k=3
-E(X)+2(26-3E(X))=3
-E(X)-6E(X)=3-52
-7E(X)=-49
E(X)=7