For each situation below, specify which distributional model would be most appro
ID: 3150409 • Letter: F
Question
For each situation below, specify which distributional model would be most appropriate for the random variable X (5 points each). Twenty students apply for a summer internship, out of which ten are in their senior year. Six students are randomly selected for interviews. Let X = how many seniors are interviewed. Let X = how many cars pass you on the highway before one of them is silver colored Let X = how long in minutes until the next 2001 Toyota Prius hybrid goes through a toll booth on the Golden Gate Bridge When you wake up tomorrow morning you look at the digital clock next to your bed and watch it until the time changes (i.e. until it changes to the next minute). Let X = how long you have to wait in minutes. The marginal distribution of X whose joint distribution with Y is given by f(x, y) = 27x^2e^-3x-2y for 0Explanation / Answer
a)
We have a limited population and we draw without replacement. Hence, we use a HYPERGEOMETRIC DISTRIBUTION MODEL, with
N = population size = 20
K = number of successes in the population = 10
n = sample size = 6
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b)
As this is the probability before one success, it is a GEOMETRIC DISTRIBUTION.
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c)
This could be a Poisson process, so the interarrival times could follow an EXPONENTIAL DISTRIBUTION.
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D)
Each time of awakening is equally probably, so this is likely to follow a UNIFORM DISTRIBUTION.
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