Keerthi

• Random variable X


  A function from the sample space S to the set of real numbers R, i.e., X : S → R
• Discrete random variable


  A random variable that can take on only a countable number of distinct values
• Continuous random variable


  A random variable that can take on any value within a specified range
• Random variables can be functions of one or more variables
• Joint cumulative probability distribution function F(a,b)


  P{X ≤ a,Y ≤ b}, -∞ < a,b < ∞
• Marginal distribution functions FX(a) and FY(b)


  FX(a) = F(a,∞) and FY(b) = F(∞,b) for any -∞ < a,b < ∞
• All joint probability statements about X and Y can be answered using their joint distribution function
• Joint probability mass function p(x,y)


  P{X = x,Y = y} for discrete random variables X and Y
• Joint probability density function f(x,y)

  For continuous random variables X and Y
• Birth phase of the lifecycle of a ReactJS component

  1. Component starts its journey on a way to the DOM

  2. Component contains the default Props and initial State

  3. Default properties are done in the constructor of a component

  4. Initial phase only occurs once
• Initial phase of a ReactJS component


  • Consists of the following methods:
• getDefaultProps()


  • Used to specify the default value of this.props
  • Invoked before the creation of the component or any props from the parent is passed into it
• getInitialState()


  • Used to specify the default value of this.state
  • Invoked before the creation of the component
• Birth phase of the lifecycle of a ReactJS component

  1. Component starts its journey on a way to the DOM

  2. Component contains the default Props and initial State

  3. Default properties are done in the constructor of a component

  4. Initial phase only occurs once
• getDefaultProps()


  • Used to specify the default value of this.props
  • Invoked before the creation of the component or any props from the parent is passed into it
• getInitialState()


  • Used to specify the default value of this.state
  • Invoked before the creation of the component
• Lifecycle of React Components

  Each React Component goes through the given Phases
• Phases of React Component Lifecycle

  1. Initialization

  2. Mounting

  3. Updating

  4. Unmounting
• Initialization phase


  • Component is constructed with the given Props and default state
  • Done in the constructor of a Component Class
• Mounting Phase


  • Rendering the JSX returned by the render method
• Updating


  • State of a component is updated and the application is repainted
• Unmounting


  • Component is removed from the page
• Each phase contains some lifecycle methods that are specific to the particular phase
• Initial Phase


  • Birth phase of the lifecycle of a ReactJS component
  • Component starts its journey on a way to the DOM
  • Component contains the default Props and initial State
• getDefaultProps()


  • Used to specify the default value of this.props
  • Invoked before the creation of the component or any props from the parent is passed into it
• getInitialState()


  • Used to specify the default value of this.state
  • Invoked before the creation of the component
• Let X be a discrete random variable which takes values 0 and 1. Y is a discrete

  random variable that takes values 0 and 1, so find joint pmf tables such that X and Y

  are independent.