ИДЗ Рябушко 18.2 Вариант 29

Solution of IDZ Ryabushko 18.2 - Option 29

Section: Chapter 18. Probability Theory
Topic: Random variables, distribution laws, numerical characteristics
Description: Construction of the distribution law of a discrete random variable, finding the distribution function and probability density, calculation of mathematical expectation, variance, standard deviation, study of normal, uniform, exponential distributions, application of Chebyshev´s inequality.

Tasks:
1. Find the distribution law of the given discrete random variable X and its distribution function F(x). Compute the mathematical expectation M(X), variance D(X) and standard deviation σ(X). Plot the graph of the distribution function F(x).
2. Given the distribution function F(x) of a random variable X. Find the probability density f(x), the mathematical expectation M(X), the variance D(X) and the probability of the random variable X falling into the interval [a; b]. Plot the graphs of the functions F(x) and f(x).
3. Solve the following problems.
4. Solve the following problems.

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