1 / 5

Random variables

Random experiment. outcome. numerical measure/aspect of outcome. Random variables. Random variable. Random variable. S. outcome. R. number. Random variables. Random variable is an assignment of a number to an outcome of a random experiment. Notation: Random variable: r.v.

jaguar
Download Presentation

Random variables

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Random experiment outcome numerical measure/aspect of outcome Random variables Random variable Random variable S outcome R number

  2. Random variables Random variable is an assignment of a number to an outcome of a random experiment. Notation: Random variable: r.v. Example. Select 13 cards from a deck of 52. Random variable X= number of Aces. Possible values of X: 0, 1, 2, 3, 4. X is a discrete r.v. Example. Select a student at random from a class of 200. Random variable X=height of the selected student. Possible values of X: [5ft, 7ft] is a continuous r.v.

  3. DISCRETE RANDOM VARIABLES Discrete r.v. takes on finite (or countable) number of values. What do we need to specify/describe a r.v? Need its values and their probabilities! We describe a discrete r.v. using probability distribution: list of all values of the random variable with the corresponding probabilities. X random variable. Values of X: x1, x2, …., xn Probabilities: P(X= x1 ) =p1, P(X= x2) =p2, …, P(X= xn ) =pn. Every pi≥0 and p1 + p2 + …+ pn =1. Typically, probability distribution of a random variable is given as a table:

  4. Discrete random variables. An example. Toss a fair coin 3 times. Let X be the number of Heads in the 3 tosses. Find the probability distribution of X. Sln. Sample space S={HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. 8 equally likely outcomes. X= # H. Possible values of X: 0, 1, 2, 3. Need probabilities. P(X=0)=P(0 Heads)=P(TTT)=1/8, (X assigned nmbr 1/8 to exprmnt outcome TTT) P(X=1)=P(1 Head)=P(TTH, THT, HTT)=3/8, P(X=2)=P(2 Heads)=P(HHT, HTH, THH)=3/8, P(X=3)=P(3 Heads)=P(HHH)=1/8. Probability distribution of X:

  5. Example, contd. • Find the probability of getting at least 1 Head; • Find the probability of getting 1 or 2 Heads. Sln. Use probability distribution of X. • P(at least 1 Head) = 1 – P( no H) = 1 – P( X=0)=1-1/8=7/8. • P(1 or 2 Heads) = P(X=1 or X=2) = P(X=1) + P(X=2)= 3/8 +3/8=6/8. Complementary events Disjoint events

More Related