Question

Случайную величину х задано функцией разпридиления F(x) найти функцию плотности разпридиления ,математическое ожидание ,дисперсию и среднее квадратическое отклонение ,построить график разпридиления и функции плостности разпридиления F(x) 0 при х<0 2sinx при 0<x<пи на 6 1 при x< пи на 6Не могу найти математическое ожидание (

Answer 1

Решение во вложенном файле

Answer 2

Finding the Probability Density Function (PDF)

The given random variable x is defined by the distribution function F(x). To find the probability density function (PDF), we can differentiate the distribution function. The PDF, denoted as f(x), is the derivative of the distribution function.

The given distribution function is: - F(x) = - 0, if x < 0 - 2sin(x), if 0 < x < π/6 - 1, if x ≥ π/6

Differentiating the distribution function in the given intervals will give us the PDF.

Mathematical Expectation (Mean)

The mathematical expectation, or mean, of a random variable is the weighted average of all possible values that the random variable can take on, where the weights are the probabilities of the values occurring.

Variance and Standard Deviation

The variance of a random variable measures how much the values of the random variable differ from the mean. The standard deviation is the square root of the variance.

Graphing the Distribution and Probability Density Function

We can graph the distribution function F(x) and the probability density function f(x) to visualize the distribution.

Let's proceed with finding the PDF, mean, variance, and standard deviation, and then graphing the distribution and PDF.