Formula: if r ~ b (r, p), then E(r)=np.

Example: Try to guess the expected value of these four questions according to the above example of guessing which box the ball is in. E(r) = np = 4×0.25 = 1 (pieces), so all four questions can be guessed correctly.

2, binomial distribution variance:

Formula: if r ~ b (r, p), then Var(r)=npq.

Example: According to the above example of guessing which box the ball is in, find the variance of these four questions.

Var(r)=npq =？ 4×0.25×0.75=0.75

Extended data

According to the definition of binomial distribution, the random variable X is the number of times that event A occurs in n Bernoulli experiments, and the probability that event A occurs in each experiment is p. Therefore, binomial distribution can be decomposed into the sum of n independent (0- 1) random variables with p as the parameter.

Let the random variable X(k)(k= 1, 2,3 ... n) obey the distribution of (0- 1), then x = x (1)+x (2)+x (3)...x (n).

Since X(k) is independent of each other, it is expected that:

Difference:

Baidu Encyclopedia-Binomial Distribution