Identify the Distribution
Select the Distribution that best fits the definition of therandom variable X in each case.
- Each hurricane independently has a certain probabilityof being classified as \"serious.\" A climatologist wants to studythe effects of the next 5 serious hurricanes. X = the number ofnon-serious hurricanes observed until the data iscollected.
- Ten percent of Netflix users watch a particular show. Asurvey asks 25 independent viewers whether they watch this show. X= the number who say yes.
- 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.
- Potholes along a road occur independently at a constantrate with no chance of two occurring at exactly the same place. X =the distance between consecutive potholes.
- Buses arrive at a certain stop EXACTLY every15 minutes. You show up at this bus stop at a random time. Let X =your waiting time until the next bus.
- A soccer player has a certain probability p of beinginjured in each game, independently of other games. X = the numberof games played before the player is injured.
- Proportions of individuals with tree blood types in apopulation are 0.2, 0.3 and 0.5 respectively. We select randomly 50individuals from a large population. What is the joint distributionof the number of individuals in the sample with the first andsecond blood type, respectively?
- A designer is working on a new ergonomic chair, andthey want it to work best for average height people, so theymeasure the heights of all 50 people working in their office. Let X= the average height.
- In Lotto 6/49 a player selects a set of six numbers(with no repeats) from the set{1, 2, ..., 49}. In the lottery draw,six numbers are selected at random. Let X = the first numberdrawn.
- A tank contains 10 tropical fish, 2 of which are a rarespecies. Five fish are removed from the tank. X = the number ofrare fish left in the tank.
