Solution of IDZ Ryabushko 18.2 - Option 1

Section: Chapter 18. Probability Theory
Topic: Random variables, distribution laws, numerical characteristics
Description: Constructing the distribution law of a discrete random variable, finding the distribution function and probability density, calculating the mathematical expectation, variance, standard deviation, studying normal, uniform, exponential distributions, applying 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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