A machine can process two online applications in 60 minutes. Answer the following questions. What would be an appropriate random variable? What would be the exponential-distribution counterpart to the random variable? Identify the mean of x, where x = minutes until the next occurrence and determine the following: P (x ≥ 30.0) P (x ≤ 10) The machine must be disconnected for service for 45 minutes. What is the probability that an online application will be sent while the machine is out of service?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A machine can process two online applications in 60 minutes. Answer the following questions.
- What would be an appropriate random variable? What would be the exponential-distribution counterpart to the random variable?
- Identify the mean of x, where x = minutes until the next occurrence and determine the following:
- P (x ≥ 30.0)
- P (x ≤ 10)
- The machine must be disconnected for service for 45 minutes. What is the probability that an online application will be sent while the machine is out of service?
Disclaimer: Only first two parts are answered.
Given that a machine processes 2 applications per hour. This process can be modeled as a Poisson process with rate
(1) Let >0 be fixed. The counting process {N(t),t∈[0,∞)}is called a Poisson process with rates if all the following conditions hold:
- N(0)=0;
- N(t) has independent increments;
- the number of arrivals in any interval of length t>0 has Poisson(λt) distribution.
The exponential distribution counterpart to the Poisson random variable is as follows:
If N(t) is a Poisson process with rate λ, then the inter arrival times X1, X2, ⋯ are independent and
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