Question

Please submit the four asterisked problems below in class on Wednesday, April 17 Be sure your work is labeled when appropriate. For example, if your solution involves "P(A)," make sure it is clear what event A is and which number in your calculation is P(A); if your solution involves a random variable X make sure it is clear what X is. 1. * An urn contains 999 red balls and 1 green ball. 2000 balls are drawn with replacement. (a) Determine the eract probability that at most 1 green ball is drawn (b) Use the Poisson approximation to determine the approrimate probability that at most 1 green ball is drawn 2. * In a certain town, the average number of bike accidents per month is 1.6. As- suming the number of bike accidents per month is a Poisson random variable: (a) What is the probability of at most 4 bike accidents in a given month? (b) What is the probability of at least 1 bike accident in a given month? (c) What is the standard deviation of the number of bike accidents in a given month? (d) In a 4-month period, what is the probability of exactly bike 5 accidents oc- curring? 3. Let else (a) Compute f(x)dx (b) Compute f(r)dx 100 HINT: How is f defined when <0

Please do questions 1 and 2

Answer 1

I. 나 X be the number of Neen ball dawn 20000 1 1999 /000 1000 b Using poisson approximation, 2- 3 + 2 = 0,406

2. 1-6 lot X be the number of bike ad mber of bike accidents in a given month, t P(x 4) 4 ! 2!3) 0.9463 2(b) P(x >1) 1-P(x) 1.6 -M 2(c) Using normal ap proximation to poisson dishibution 2(d) For 4 month period, :. Iuquired Probability = P(x=5)= Ne- sl (64)sx e-64 120 = 0.1486 D.148