SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Random Variables & Probability Distributions

layne avatar
layne
11 diapositives · 329 Views · Jul 20, 2014

Random Variables & Probability Distributions. “The probability of someone laughing at you is proportional to the stupidity of your actions.”. Definitions Random Variable: A variable whose possible values are numerical outcomes of a random phenomenon Discrete Random Variable:

Random Variables & Probability Distributions - slide 1
01 / 11Random Variables & Probability Distributions
1 / 17

Télécharger la présentation

Random Variables & Probability Distributions
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Random Variables & Probability Distributions “The probability of someone laughing at you is proportional to the stupidity of your actions.”

  2. Definitions Random Variable: A variable whose possible values are numerical outcomes of a random phenomenon Discrete Random Variable: Has a countable number of outcomes; distribution described by a histogram Continuous Random Variable: Takes all values in an INTERVAL of numbers; distribution described by a density curve (i.e., normal curve)

  3. Definitions Sample Space: Set of all possible outcomes Probability Distribution: A chart that lists the values of the discrete random variable X and the probability that X occurs; all probabilities add up to 1; can graph as a histogram

  4. Expected Value of a Discrete Random Variable Expected Value = mean = *this is the sum of the products of x and P(x) from the probability distribution

  5. Example 1: State whether each of the following random variables is discrete or continuous: • a) The number of defective tires on a car. • discrete • b) The body temperature of a hospital patient. • continuous • c) The number of pages in a book. • discrete • d) The lifetime of a light bulb. • continuous

  6. Example 2: Let X denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a certain market. Suppose that the probability distribution of X is as follows: • a) Interpret P(X = 1) =.20. • The probability that there is 1 broken egg is .20. • b) Find the probability that there are exactly 4 broken eggs. • P(X = 4) = .01 • c) Find the probability that there are at least 2 broken eggs. • P(X = 2 or X = 3 or X = 4) = .10 + .04 + .01 = .15 • d) Find the probability that there are less than 2 broken eggs. • P(X = 0 or X = 1) = .65 + .20 = .85 • e) How many eggs should we “expect” to be broken? • E(X) = 0(.65) + 1(.20) + 2(.10) + 3(.04) + 4(.01) =

  7. Example 3. Suppose we flip a coin 3 times. Let X = the number of heads. • Write the sample space of flipping the coin. • HHH • HHT • HTH • THHHTT • THT • TTH • TTT

  8. Example 3. b) Determine the probability distribution.

  9. Example 3. • c) Sketch a histogram of the probability distribution.

  10. Example 3. • d) How many heads would we “expect”? • E(X) =

  11. Example 4: Suppose we toss two dice and sum the results. a) Write out the sample space b) Determine the probability distribution. c) What is the probability you get a sum less than 5? d) What is the probability you get a sum of at least 10? e) What is the expected value of the sum of the two dice?