Consider the random variable G = the amount of time between goals in a soccer ga

Question

Consider the random variable G = the amount of time between goals in a soccer game. The mean time between goals is 30 minutes. The probability distribution of G is exponential.
Answer the following questions. Use decimals for your answers, and when necessary round answers to 4 decimal places.
What is the decay constant m?
What is the probability that the time between goals is less than 10 minutes?
Calculate P(G > 90), which is the probability that no goals are scored in regulation.
What is the mean of the distribution of G?
What is the standard deviation of the distribution of G?

Explanation / Answer

decay constant m =1/mean time =1/30

probability that the time between goals is less than 10 minutes =P(X<10)=1-e-mt =1-e-10/30 =0.2835

probability that no goals are scored in regulation =P(G>90) =e-90/30 =0.0498

mean of the distribution of G =30 minutes

standard deviation of the distribution of G =30 minutes

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.