2. If X is a discrete random variable, all its possible values are a 1, a2, …, an, …, and the corresponding probabilities are p 1, p2, …, pn, …, then its mathematical expectation E (x) = (A1) (P
Expectation of uniform distribution: The expectation of uniform distribution is the midpoint (a+b)/2 of the value interval [a, b]. ?
Variance of uniform distribution: var(x)=E[X? ]-(E[X])？ .
Extended data:
Variables can only take discrete natural numbers, that is, discrete random variables. For example, if you toss 20 coins at a time, K coins face up, and K is a random variable. The value of k can only be natural number 0, 1, 2, …, 20, but not decimal number 3.5 or irrational number, so k is a discrete random variable.
If a variable can take any real number in a certain interval, that is, the value of the variable can be continuous, then this random variable is called a continuous random variable. For example, the bus runs every 15 minutes, and the waiting time of people on the platform is a random variable. The value range of X is [0, 15], which is an interval. Theoretically, any real number 3.5, irrational number, etc. Can be taken in this interval, so this random variable is called continuous random variable.