Question

Identify the Distribution

Select the Distribution that best fits the definition of the random variable X in each case.

1. Each hurricane independently has a certain probability of being classified as "serious." A climatologist wants to study the effects of the next 5 serious hurricanes. X = the number of non-serious hurricanes observed until the data is collected.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

2. Ten percent of Netflix users watch a particular show. A survey asks 25 independent viewers whether they watch this show. X = the number who say yes.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

3. The number of car accidents at a particular intersection occur independently at a constant rate with no chance of two occurring at exactly the same time. X = the number of accidents on a Thursday.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

4. Potholes along a road occur independently at a constant rate with no chance of two occurring at exactly the same place. X = the distance between consecutive potholes.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

5. Buses arrive at a certain stop EXACTLY every 15 minutes. You show up at this bus stop at a random time. Let X = your waiting time until the next bus.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

6. A soccer player has a certain probability p of being injured in each game, independently of other games. X = the number of games played before the player is injured.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

7. Proportions of individuals with tree blood types in a population are 0.2, 0.3 and 0.5 respectively. We select randomly 50 individuals from a large population. What is the joint distribution of the number of individuals in the sample with the first and second blood type, respectively?

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

8. A designer is working on a new ergonomic chair, and they want it to work best for average height people, so they measure the heights of all 50 people working in their office. Let X = the average height.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

9. 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 number drawn.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

10. A tank contains 10 tropical fish, 2 of which are a rare species. Five fish are removed from the tank. X = the number of rare fish left in the tank.

	Discrete Uniform
	Hypergeometric
	Binomial
	Negative Binomial
	Geometric
	Poisson
	Continuous Uniform
	Exponential
	Normal
	Multinomial
	None of the Above

Answer 1

Q.1. Let "p" be the probability of the hurricane being serious, and "q" be the probability of the hurricane being nonserious.

X is defined as the number of nonserious hurricanes observed until the data is collected.

Therefore, x follows Geometric distribution.

Q.2. let "p " be the probability of Netflix users watching a particular show. i.e p=.1

Let "q" be the probability of users not watching a particular show. i.e., q=.9

x is defined as the number of users who watch that particular show. n=25

therefore x follows binomial distribution i.e X~ Bin(25,.1)

Q.3. It is mentioned that no. of accidents occur independently at a constant rate.

And x is defined as the number of accidents on a Thursday.

Since the rate is constant and independent, and the random variable X is discrete.

X follows a Poisson distribution

Q.4. Mentioned that Potholes along a road occur independently at a constant rate with no chance of two occurring at exactly the same place.

And X is defined as the distance between two consecutive potholes.

since the rate of occurrence of the potholes are constant and independent and the random variable X is continuous

X follows an exponential distribution.

Q.5 X follows a continuous uniform distribution

Q.6. X Follows geometric distribution.

Q,7 X Follows multinomial distribution

q.8. X follows normal distribution

q.9 X follows a Discrete uniform Distribution

q.10 X follows a hypergeometric distribution