Question 2: Exponential distribution The time (X) that an infected patient with COVID19 may infects other...

Question 2: Exponential distribution

The time (X) that an infected patient with COVID19 may infects other people in a gathering, if he/she is not wearing a mask, is exponentially distributed with mean (µ= 6) minutes. Answer the following questions:

What is the probability that an infected and unmasked patient infects others in less than 5 minutes?
What is the probability that an infected and unmasked patient infects others in more than 10 minutes?
The Department of Health stated that there is 90% chance that a healthy individual will be infected by an infected and unmasked patient in less than 15 minutes in a gathering. Check if the Department of Health is correct. Show your work.
If the mean time to infect a healthy individual (µ) by an unmasked infected patient is unknown, but we know that the probability that the time to infect a healthy individual to be more than 20 minutes is 0.41. What was the mean time to infect a healthy individual?

Expert Solution

orchestra answered 2 years ago

The life time X of a component, costing $1000, is modelled using an exponential distribution with...

The life time X of a component, costing $1000, is modelled using an exponential distribution with a mean of 5 years. If the component fails during the first year, the manufacturer agrees to give a full refund. If the component fails during the second year, the manufacturer agrees to give a 50% refund. If the component fails after the second year, but before the fifth year the manufacturer agrees to give a 10% refund. (a) What is the probability that...

The time between car arrivals at an inspection station follows an exponential distribution with V (x)...

The time between car arrivals at an inspection station follows an exponential distribution with V (x) = 22 minutes. 1) Calculate the probability that the next car will arrive before the next 10 minutes. 2) Calculate the probability of receiving less than 5 cars during the next hour 3) If more than half an hour has passed without a car being presented, what is the probability that the employee will remain unemployed for at least 10 minutes? 4) If the...

An exponential distribution is formed by the time it takes for a person to choose a...

An exponential distribution is formed by the time it takes for a person to choose a birthday gift. The average time it takes for a person to choose a birthday gift is 41 minutes. Given that it has already taken 24 minutes for a person to choose a birthday gift,what is the probability that it will take more than an additional 34 minutes?

The time until failure for an electronic switch has an exponential distribution with an average time...

The time until failure for an electronic switch has an exponential distribution with an average time to failure of 4 years, so that λ = 1 4 = 0.25. (Round your answers to four decimal places.) (a) What is the probability that this type of switch fails before year 3? (b) What is the probability that this type of switch will fail after 5 years? (c) If two such switches are used in an appliance, what is the probability that...

The waiting time until a courier is received is followed by an exponential distribution with an...

The waiting time until a courier is received is followed by an exponential distribution with an expected waiting time of 5 days. Find the probability that the mean waiting time for the delivery time of 50 couriers exceeds 6 days b. There are 200 questions to an FRCS exam. Suppose the probability of having through question correct is 0.6, no matter other questions. If the cutoff for a grade B is 80%, what is the likelihood of a "B"

Consider an exponential distribution f(x|θ) = θe^(−θx) for x > 0. Let the prior distribution for...

Consider an exponential distribution f(x|θ) = θe^(−θx) for x > 0. Let the prior distribution for θ be f(θ) = e^ −θ for θ > 0. (a) Show that the posterior distribution is a Gamma distribution. With what parameters? (b) Find the Bayes’ estimator for θ.

This is the code in R for the Central Limit theorem question. This is Exponential distribution...

This is the code in R for the Central Limit theorem question. This is Exponential distribution with mean beta. How can I modify this code to Bernoulli(0.1), Uniform (0,4), and Normal distribution (2,1) plot.z <- function(n, m=1e5, beta = 1) { mu <- beta sigma <- beta zs <- rep(0,m) for(i in 1:m) { Y.sample <- rexp(n, 1/beta) Ybar <- mean(Y.sample) zs[i] <- (Ybar - mu) / (sigma / sqrt(n)) } p <- hist(zs, xlim=c(-4,4), freq = F, main =...

-Event time T follows an exponential distribution with a mean of 40 -Censoring time Tc follows...

-Event time T follows an exponential distribution with a mean of 40 -Censoring time Tc follows an exponential distribution with a mean of 25 -Generate 500 observations, with censoring flag indicating whether censoring happened before events Question: What do you think the percent of censoring should be? Show your calculation or reasoning.

The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X...

The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X > 12) is equal to

A certain type of pump’s time until failure has an exponential distribution with a mean of...

A certain type of pump’s time until failure has an exponential distribution with a mean of 5000 hours. State answers rounded to two decimal places. What is the probability it will still be operating after 3000 hours of service? What is the probability that it will fail prior to 6000 hours of service? If it has been running for 3000 hours, what is the probability it will still be running 2000 hours later?

Question