Question

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)?

Answer 1

`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`