ZuoTi.Pro
Question

Suppose X has a Poisson distribution with a mean of 7. Determine the following probabilities Round your answers to four decimal places (e.g. 98.7654) (a) P(X- o.0025 (b) P(X 2) = 0446 (c) P(X-4.1338 (d) P(x- 8.103:3

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

Solution:

a)

P(0) Probability of exactly 0 occurrences If using a calculator, you can enter A-7and x 0 into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: where x is the number of occurrences, λ is the mean number of occurrences, and e is the constant 2.718. Substituting in values for this problem, x = 0 and λ 7, we have Evaluating the expression, we have P(0 0.0009

b)

Solution: P(X 2) Probability of at most 2 occurrences At most 2 occurrences includes X-values of X 0, 1, 2. To solve this problem, find the sum of the poisson probabilities for each of the values of X, or if there is only one value of X, find the probability of P(X). In this problem, To find the individual probabilities for each occurrence, X, you can either use a caluclators poisson probability distribution function (PDF), or you can use the poisson probability formula for each occurrence, X. Then, find the sum of each of the individual probabilities Some calculators have a cumulative poisson probability function (CDF). For at most questions like these, you may use the calculators cumulative poisson probability function and enter X 7 and r -2. This is a one step process to get the final answer to this question.Find the First Probability P(O) For the probability P(0), you can enter A 7 and 2 into a poisson probability distribution function (PDF). The answer is P(0) 0.00091188196555452. If youre not using a calculator, apply the poisson probability formula e- where x is the number of occurrences, A is the mean number of occurrences, and e is the constant 2.718. Substituting in values for this problem, 0 and A7, we have Remember, O! is 1. Evaluating the expression, we have P(0 0.00091188196555452

Find the Remaining Probabilities To calculate any remaining probabilities, we need to either use the poisson probability distribution function on a calculator or the poisson probability formula. Well add these remaining probababilities to P(O) for our final answer. 0.00091188196555452+ 0.0063831737588816+ 0.022341108156086 0.0296c)

Solution: P(4) Probability of exactly 4 occurrences If using a calculator, you can enter A7 and 4 into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: where x is the number of occurrences, λ is the mean number of occurrences, and e is the constant fs bm4 nd A -7.we hae e-7.74 P(4)--41 Evaluating the expression, we have P(4) 0.0912d)

Solution: P(8) Probability of exactly 8 occurrences If using a calculator, you can enter A 7 and 8 into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula Pr! where x is the number of occurrences, A is the mean number of occurrences, and e is the constant 2.718. Substituting in values for this problem, z 8 and A-7, we have 8! Evaluating the expression, we have P(8) 0.1303

1 0
Add a comment
Know the answer?
Add Answer to:
Suppose X has a Poisson distribution with a mean of 7. Determine the following probabilities Round...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT