Question

In: Statistics and Probability

For the last 40 years there have been 135 manned space flights. The missions were random,...

For the last 40 years there have been 135 manned space flights. The missions were

random, independent, and uniformly spread out over the time interval. Suppose we want to

know the probability that 10 manned space flights will happen in the next 40 years. (Do not

calculate this.)

What discrete distribution would best fit this problem? Briefly explain. (i.e. what conditions

are met?)

Solutions

Expert Solution

Poisson distribution would best fit this problem, because for a distribution to be a poisson distribution, following conditions are need to be met.

  • An event can occur any number of times during a time period. i.e. 10 times in 40 yesars
  • Events occur independently. In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. Given that the missions were random and independent
  • The rate of occurrence is constant; that is, the rate does not change based on time. rate is 10 times in 40 years
  • The probability of an event occurring is proportional to the length of the time period. For example, it should be twice as likely for an event to occur in a 2 hour time period than it is for an event to occur in a 1 hour period.

orchestra answered 1 year ago
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