Roll the dice 100 times and find the mathematical expectation and variance of the sum of points.

The expected number of dice X is (1+2+3+4+5+6)/6 = 3.5; e(X)=( 1+4+9+ 16+25+36)/6 = 15. 167； DX = 15. 167-3.5 square = 2.9 166667.

Sum of expected points y ey = n * 3.5 variance dy = n * dx = 2.9 1666667n

Extended data

Probability theory and mathematical statistics based on it play an indispensable role in many fields such as natural science, social science, engineering technology, military science and industrial and agricultural production.

Intuitively speaking, satellites in the sky, missile cruises, aircraft manufacturing, spacecraft traveling in space, etc. Have the contribution of probability theory; Timely and accurate weather forecast, ocean exploration and archaeological research are inseparable from probability theory and mathematical statistics; The development of electronic technology, the progress of film and television culture, population census and educational equivalent probability theory are also inseparable from mathematical statistics.

Monte Carlo method is a calculation method based on probability theory and mathematical statistics. With the help of computer, this method plays an important role in the research of nuclear physics, surface physics, electronics, biology, polymer chemistry and other disciplines.

As a branch of mathematics with rigorous theory and wide application, probability theory has attracted more and more attention and will develop with the development of science and technology.