MathProblemsBank Math Problems Bank
  • Home
  • Forum
  • About Us
  • Contact Us
  • Login
  • Register
  • language
 MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Mathematics sections
  • Algebra
    • Vector Algebra
    • Determinant calculation
    • Permutation group
    • Matrix transformations
    • Linear transformations
    • Quadratic forms
    • Fields, Groups, Rings
    • Systems of algebraic equations
    • Linear spaces
    • Polynomials
    • Tensor calculus
    • Vector analysis
  • Analytic geometry
    • Curves of the 2-nd order
    • Surfaces of the 2-nd order
    • Lines on a plane
    • Line and plane in space
    • Tangents and normals
  • Complex analysis
    • Operations with complex numbers
    • Singular points and residues
    • Integral of a complex variable
    • Laplace transform
    • Conformal mappings
    • Analytic functions
    • Series with complex terms
    • Calculating integrals of a real variable using residues
  • Differential equations
    • Ordinary differential equations
      • First order differential equations
      • Second order differential equations
      • Higher order differential equations
      • Geometric and physical applications
    • Systems of ordinary differential equations
    • Stability
      • Stability of the equations
      • Stability of the systems of equations
    • Operating method
      • Differential equations
      • Systems of differential equations
  • Differential geometry
  • Discret mathematics
    • Boolean algebra
    • Set theory
    • Combinatorics
    • Graph theory
    • Binary relations
    • Propositional algebra
      • Propositional calculus
      • Sequent calculus
    • Predicate calculus
    • Theory of algorithms and formal languages
    • Automata theory
    • Recursive functions
  • Functional analysis
    • Metric spaces
      • Properties of metric spaces
      • Orthogonal systems
      • Convergence in metric spaces
    • Normed spaces
      • Properties of normed spaces
      • Convergence in normed spaces
    • Measure theory
      • Lebesgue measure and integration
      • Measurable functions and sets
      • Convergence (in measure, almost everywhere)
    • Compactness
    • Linear operators
    • Integral equations
    • Properties of sets
    • Generalized derivatives
    • Riemann-Stieltjes integral
  • Geometry
    • Planimetry
      • Transformations on the plane
      • Construction problems
      • Complex numbers in geometry
      • Various problems on the plane
      • Locus of points
    • Stereometry
      • Construction of sections
      • Various problems in the space
    • Affine transformations
  • Mathematical analysis
    • Gradient and directional derivative
    • Graphing functions using derivatives
    • Plotting functions
    • Fourier series
      • Trigonometric Fourier series
      • Fourier integral
    • Number series
    • Function extrema
    • Power series
    • Function properties
    • Derivatives and differentials
    • Functional sequences and series
    • Calculation of limits
    • Asymptotic analysis
  • Mathematical methods and models in economics
  • Mathematical physics
    • First order partial differential equations
    • Second order partial differential equations
      • d'Alembert method
      • Fourier method
      • With constant coefficients
      • With variable coefficients
      • Mixed problems
    • Convolution of functions
    • Nonlinear equations
    • Sturm-Liouville problem
    • Systems of equations in partial derivatives of the first order
  • Mathematical statistics
  • Numerical methods
    • Golden section search method
    • Least square method
    • Sweep method
    • Simple-Iteration method
    • Approximate calculation of integrals
    • Approximate solution of differential equations
    • Approximate numbers
    • Function Interpolation
    • Approximate solution of algebraic equations
  • Olympiad problems
    • Olympic geometry
    • Number theory
    • Olympic algebra
    • Various Olympiad problems
    • Inequalities
      • Algebraic
      • Geometric
    • Higher mathematics
  • Probability theory
    • One dimensional random variables and their characteristics
    • Theory of random processes
    • Markov chains
    • Queuing systems
    • Two-dimensional random variables and their characteristics
    • Definition and properties of probability
    • Limit theorems
  • Real integrals
    • Integrals of functions of a single variable
      • Indefinite integrals
      • Definite Integrals
      • Improper integrals
    • Double integrals
    • Triple integrals
    • The area of a region
    • Volume of a solid
    • Volume of a solid of revolution
    • Flux of the vector field
    • Surface integrals
    • Curvilinear integrals
    • Potential and solenoidal fields
    • Vector field circulation
    • Integrals depending on a parameter
  • Topology
  • USE problems
  • Variational calculus
Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Find the solution of the first-order partial differential equation under the given conditions: \[ (1+\sqrt{z-x-y}) \cdot \frac{\partial z}{\partial x}+x \frac{\partial z}{\partial y}=2, \quad z=x \text { when } y=0 . \]

11.4.41 First order partial differential equations

3.82 $

Problem: Find the surface that satisfies the first-order partial differential equation under the given conditions: \[ x \frac{\partial z}{\partial x}-y \frac{\partial z}{\partial y}=z^{2}(x-3 y), x=1, \quad y z+1=0 . \]

11.4.42 First order partial differential equations

3.31 $

Problem: Find the surface that satisfies the first-order partial differential equation under the given conditions: \[ (y-z) \frac{\partial z}{\partial x}+(z-x) \frac{\partial z}{\partial y}=x-y, \quad z=y=-x . \]

11.4.43 First order partial differential equations

3.82 $

Problem: Find the surface that satisfies the first-order partial differential equation under the given conditions: \[ x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=z-x y, \quad x=2, \quad z=y^{2}+1 . \]

11.4.44 First order partial differential equations

3.82 $

Problem: The probability that the element has passed the QC is equal to 0,8. Estimate by Chebyshev's inequality the probability that among 400 randomly chosen elements there will be from 60 to 100 unverified elements. Specify the result with the help of Laplace integral theorem.

15.2.31 One dimensional random variables and their characteristics

3.05 $

Problem: Random errors in measuring the distance to the fixed target are subject to the normal law of distribution with the expected value of \( a=5 \mathrm{~m} \) and the dispersion \( \sigma^{2}=100 \mathrm{~m}^{2} \). Determine the probability that: a) the measured value of the distance deviates from the true value by more than \( 15 \mathrm{~m} \). b) for three independent measurement the error of at least one measurement will not exceed \( 15 \mathrm{~m} \) in the absolute value.

15.2.32 One dimensional random variables and their characteristics

2.54 $

Problem: The random variable \( X \) a distribution, the probability density of which is \( f(X)=\frac{\lambda}{2} e^{-\lambda|x|}(\lambda>0) \). Find the expected value and the dispersion of the random variable \( Z=2+0,5 X \).

15.2.33 One dimensional random variables and their characteristics

2.04 $

Problem: Let \( \xi_{1}, \cdots, \xi_{n} \) are independent identically distributed random variables, with finite dispersion \( \sigma^{2} \). Let's designate \[ \bar{\xi}=\frac{\xi_{1}+\cdots+\xi_{n}}{n} . \] Find the expected value of the random variable \[ \frac{1}{n-1} \sum_{k=1}^{n}\left(\xi_{k}-\bar{\xi}\right)^{2} . \]

15.2.34 One dimensional random variables and their characteristics

6.36 $

Problem: Let \( \xi \) is a random variable with a symmetrical distribution. Let's substitute \[ \eta=\left\{\begin{array}{l} \xi, \text { when }|\xi| \leq c \\ 0, \text { when }|\xi|>c \end{array}, c>0 .\right. \] Let's denote \( f(t) \) and \( g(t) \) are the characteristic functions of \( \xi \) and \( \eta \) respectively. Prove that there will be such \( \varepsilon>0 \), that \( f(t) \leq g(t) \), when \( |t| \leq \varepsilon \).

15.2.35 One dimensional random variables and their characteristics

3.82 $

Problem: It's known that for independent random variables \( X_{1}, \cdots, X_{4} \) their expected values are \( E\left(X_{i}\right)=-2 \), the dispersions are \( D\left(X_{i}\right)=1 \), \( i=1, \cdots, 4 \). Find the dispersion of the product \( D\left(X_{1} ; \cdots X_{4}\right) \).

15.2.36 One dimensional random variables and their characteristics

0 $

Problem: The probability of a stock rising by \( 3 \% \) in one working day is equal to 0,1 , the probability of rising by \( 0,1 \% \) is equal to 0,6 , and the probability of decrease by \( 1 \% \) is equal to 0,3 . Find the expected value of the change of the stock in 100 working days, taking into account that the initial stock is 1000 dollars, and the relative price changes for different working days are independent random variables.

15.2.37 One dimensional random variables and their characteristics

1.78 $

Problem: The random variable \( X \) is uniformly distributed on the segment \( [-3,11] \). Find the probability \[ P\left(\frac{1}{X-3}>4\right) \text {. } \]

15.2.38 One dimensional random variables and their characteristics

1.02 $

Problem: The random variable \( X \) is uniformly distributed on the segment \( [-4,2] \). Find \( E\left(e^{4 X}\right) \).

15.2.39 One dimensional random variables and their characteristics

0 $

Problem: The random variable \( X \) is distributed in accordance with the exponential law. Find the expected value \( E\left\{(X+8)^{2}\right\} \), if the dispersion \( D(X)=36 \).

15.2.40 One dimensional random variables and their characteristics

1.02 $

Problem: The student answers three questions on the examination card. The probability of a correct answer to the first question is equal to 0,5 , to the second one is 0,7 and to the third question 0,9 . It is required: a) make a distribution series of the number \( X \) of the questions, which are given correct answers; b) find the expected value and the dispersion of the random variable \( X \); c) accurately plot the graph of its function of the distribution \( F_{X}(x) \).

15.2.41 One dimensional random variables and their characteristics

3.05 $

  • ‹
  • 1
  • 2
  • ...
  • 88
  • ...
  • 116
  • 117
  • ›

mathproblemsbank.net

Terms of use Privacy policy

© Copyright 2025, MathProblemsBank

Trustpilot
Order a solution
Order a solution to a problem?
Order a solution
Order a solution to a problem?
home.button.login