(2)、e(y)=∫(-∞,+∞)f(x)e^(-2x)dx= 1/3

Expectation is not necessarily equal to "expectation" in common sense-expectation is not necessarily equal to every result. The expected value is the average of the output values of variables. The expected value is not necessarily contained in the set of output values of variables.

If a random variable only takes a finite number of values or can be listed in a certain order, its range of values is one or several finite or infinite intervals, such a random variable is called a discrete random variable.

Extended data:

Let the random variable X have the probability density fX(x),-∞

Simply talking about probability density has no practical significance and must be based on a certain bounded interval. The probability density can be regarded as the ordinate, and the interval is the abscissa. The integral of the probability density to the interval is the area, which is the probability of the event occurring in this interval, and the sum of all the areas is 1. Therefore, it is meaningless to analyze the probability density of a point alone, and there must be an interval for reference and comparison.

Baidu Encyclopedia-Mathematical Expectation