So xy is also a discrete random variable.

Find the probability distribution list of xy first.

Find the expectation of xy again

take for example

P(x=0)= 1/2，P(x= 1)= 1/2

P(y=0)= 1/2，P(y= 1)= 1/2

Then p (xy = 0) = 3/4.

P(xy= 1)= 1/4

Therefore, e (xy) = 0× (3/4)+/kloc-0 /× (1/4) =1/4.

If all possible values of random variable X are finite or infinite, then the range of its distribution function is discrete, and the corresponding distribution is also discrete. Commonly used discrete distributions include binomial distribution, Poisson distribution, geometric distribution, negative binomial distribution and so on.

Extended data:

Discrete random variables have finite or countable values in a certain interval. For example, the number of births and deaths in a certain area in a certain year, the effective number and ineffective number of a certain drug in treating a certain patient, etc.

The advantage of quantifying random events is that random phenomena can be studied through mathematical analysis. For example, the number of passengers waiting at the bus stop in a certain period of time, the number of calls received by the telephone exchange in a certain period of time, the life of the light bulb and so on. , are examples of random variables.

In practical problems, it is often used to represent the probability characteristics of multiple independent random test results or multiple independent random factors, so it is very important for the application of probability statistics.

Baidu Encyclopedia-Random Variable