Identify the Distribution
Select the Distribution that best fits the definition ofthe random variable X in each case.
Question 1) You have 5 cards in a pile, including onespecial card. You draw 3 cards one at a time without replacement. X= the number of non-special cards drawn.
Question 2) The number of car accidents at a particularintersection occur independently at a constant rate with no chanceof two occurring at exactly the same time. X = the number ofaccidents on a Thursday.
Question 3) A soccer player has a certain probability pof being injured in each game, independently of other games. X =the number of games played before the player isinjured.
Question 4) A jury of 12 people each independently voteon whether a defendant is guilty or not guilty, each with the sameprobability. X = the number who vote guilty.
Question 5) In a single game of (American) roulette, asmall ball is rolled around a spinning wheel in such a way that itis equally likely to land in any of 38 bins. Sixteen of the binsare Red, another 16 are Black, and the remaining 2 are Green.Suppose 5 games of roulette are to be played. What is the jointdistribution of the number of times the ball lands Red and thenumber of times the ball lands Green?
Question 6) Each hurricane independently has a certainprobability of being classified as \"serious.\" A climatologist wantsto study the effects of the next 5 serious hurricanes. X = thenumber of non-serious hurricanes observed until the data iscollected.
Question 7) The amount of anesthetic required to keep aperson asleep during a 1-hour surgery is directly related to theirweight. A hospital is performing 10 such surgeries on 10independent patients. X = the total amount of anestheticrequired.
| Discrete Uniform |
| Hypergeometric |
| Binomial |
| Negative Binomial |
| Geometric |
| Poisson |
| Continuous Uniform |
| Exponential |
| Normal |
| Multinomial |
| None of the Above |
Question 8) To measure the concentration of chemicals inrain, a square of absorbant paper is placed outside in a rainstormfor a few seconds, where raindrops are equally likely to landanywhere on it. X = the x-coordinate of a random raindrop on thepaper.
Question 9) In Lotto 6/49 a player selects a set of sixnumbers (with no repeats) from the set {1, 2, ..., 49}. In thelottery draw, six numbers are selected at random. Let X = the firstnumber drawn.
Question 10) Emails arrive at a server independently ofeach other at the uniform rate throughout the day with littlechances of more than one email arriving at the same instant. X =time between two consecutive emails.
