Name the probability distribution functions typically associated with: Rolling a
ID: 456274 • Letter: N
Question
Name the probability distribution functions typically associated with:
Rolling a die
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Tossing a coin
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Number of customer arrivals per time period (or arrival rate)
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Number of calls arriving at a call center per time period (or arrival rate)
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Inter-arrival times for calls received at a call center
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Inter-arrival times for customers arriving at a restaurant
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Waiting time until the next customer arrival at a restaurant
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Service-times of customers
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Bell-curve
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Gauss
[ Choose ] Discrete uniform distribution Normal Distribution Poisson Distribution Exponential Distribution
Explanation / Answer
a) Rolling a dice is the discrete uniform distribution. A random variable X follows the discrete uniform distribution on the interval [a, a+1, . . . , b], if it may attain each of these values with equal probability. Hence in case of rolling a dice the probability of getting any number is same i.e. 1/6. The possible number also lies in the set [1,2,3,4,5,6].
b) Toss a fair coin describes a discrete function with equal probabilities of getting head or tail. More precisely, tossing a coin generates 2 cases success or failure with probability p and 1-p hence it shows binomial distribution.
c) The number of customers arriving per time period describes Poisson distribution. The arrival of a customer is completely independent of the arrival of other customers. Poisson distribution defines the set of independent occurrence of events in a given period of time hence arrival rate follows the Poisson distribution.
d) The number of calls arriving at a call center per time period also follows Poisson distribution for the same explanation as above since the arrival rates of calls are independent of each other and occurs in a fixed time period.
e) Inter-arrival times for calls received at a call center follows an exponential distribution. The time between successive incoming calls at a call center, or between successive patrons entering a store. These “interarrival” times are typically exponentially distributed.
f) Inter-arrival times for customers arriving at a restaurant also follows an exponential distribution. As explained above, these “interarrival” times are typically exponentially distributed.
g) Waiting time until the next customer arrives at a restaurant follows an exponential distribution. The exponential distribution is often concerned with the amount of time until some specific event occurs. The time spent waiting between events is often modeled using the exponential distribution.
h) Service-times of customers follows an exponential distribution since exponential distribution is often concerned with the amount of time until some specific event occurs.
i) Bell curve follows the normal distribution.
j) Gauss also follows the normal distribution.
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