Untitled Quiz
6 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula to calculate the expected value of a discrete random variable?

  • ∑xP(x) (correct)
  • ∑x^2 - P(x)
  • ∑x^2P(x)
  • ∑P(x)/x

    • If X is a discrete random variable and Y = X^2, what is E(Y)?

  • E(X^3)
  • E(X)^4
  • E(X^2) (correct)
  • E(X)^2

    • What is the variance of a binomial distribution with n trials and probability of success p?

  • np
  • n/p
  • n(1-p)
  • np(1-p) (correct)

    • What is the probability of getting exactly 2 successes in 10 trials, where the probability of success is 0.5?

    <p>0.205</p> Signup and view all the answers

    What is the meaning of P(X ≤ 3) in a Poisson distribution?

    <p>The probability of getting at most 3 successes</p> Signup and view all the answers

    What is the formula to calculate the variance of a discrete random variable?

    <p>E(X^2) - E(X)^2</p> Signup and view all the answers

    Study Notes

    Discrete Probability Distribution

    • A discrete probability distribution table is given with values of x (0, 1, 2, 3, 4) and their corresponding probabilities (1/5, 1/5, 1/5, 1/5, 1/5)
    • The expected value and variance of the discrete random variable need to be determined

    Fair Die

    • A normal 6-sided fair die is thrown 24 times and the number of 6's scored is recorded
    • The mean and variance of the experiment need to be calculated

    Random Variable X

    • Random variable X takes values -1, 0, 1 with probabilities 1/8, 2/8, 5/8 respectively
    • Need to compute E(X) and Var(X)
    • Y = X^2, need to compute pmf of Y and E(Y)

    Discrete Random Variable X

    • X has a probability mass function (PMF) with values x = 1, 2, 3, 4 and probability cx, and x = 5 with probability 1/2
    • Need to find the value of constant c, E(3X + 2) and Var(3X + 2)

    Poisson Distribution

    • X ~ Po(0.2), need to determine the following probabilities:
      • P(X ≤ 3)
      • P(X = 6)
      • P(X > 0)

    Binomial Distribution

    • X ~ B(n = 10, p = 0.5), need to determine the following probabilities:
      • P(X ≤ 2)
      • E(X) and Var(X)

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Chapter 4 Tutorial Set Questions PDF

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser