Solution: Write the expectation and variance of X first, and then use the nature of mathematical expectation to transform E{X+e -2X} into the sum of two expectations and calculate them separately.

/& gt； ∵X obeys the exponential distribution with the parameter 1,

Probability density function f(x)= 1

e-x，x>0

0，x≤0，

And EX= 1, DX= 1,

∴Ee-2x=

∫+∞0e-2x？ e-xdx=-

1

3e-3x

|+∞0=

1

3,

So: E(X+e-2X)=EX+Ee-2X= 1+

1

3=

four

3.

Comments:

Test site of this question: exponential distribution.

Test center comments: This question examines the probability density function of exponential distribution and its expectation, as well as the nature of expectation. For common distribution functions, we should remember its expectation and variance.