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- Suppose that X₁, the number of particles emitted in t hours from a radio - active source has a Poisson distribution with parameter 20t. What is the probability that exactly 5 particles are emitted during a 15 minute period?Suppose the number of typographical errors on a single page of your book has a Poissondistribution with parameter λ = 1/2. Calculate the probability that there is at least one error onthis pageQ3. Suppose that X;i, i = 1,2, .,n have an Exponential distribution with parameter 2. a) Find maximum likelihood estimator (Â) for 2. b) Is â is an unbiased estimator?
- 7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determines the number of missing/corrupted packets. Suppose that number X has a Poisson distribution with parameter 23. = (a) What is the probability that the counter determines that the transmission has exactly one miss- ing/corrupted packet of data? (b) What is the probability that the counter determines that the transmission has at least 3 miss ing/corrupted packets of data? (c) If two transmissions of data across the internet ar that at least one of them does not contain a missing/corrupted packet? e independently selected, what is the probabilityThe entire human genome can be considered to a long book broken into pages. Suppose that the number ofmutations on a single page of this book has a Poisson distribution with parameter λ = 1/2 . For a given page, calculate that there are atleast 2 mutations on the page?5. A particular drug company claims that its headache remedy stops the average headache in 14 minutes. Being skeptical, you think they are exaggerating the speed at which their medication works. You randomly select 25 headache patients, and record the length of time it takes for their headache to disappear after taking the company's medication. The results of your study are = 19 minutes and s = 7. Assume that the length of time is normally distributed. Carry out a hypothesis test to try to prove your suspicion, using a = 0.1 6. Find the p-values for each test below, assuming that o is known, and therefore the test statistic follows a standard normal distribution: a) Ho u=50 Ha : µ > 50 test statistic = –0.13 %3D p(Z>-0.13) P malue = 0.5517 b) Ho : µ = 0 Ha : µ +0 test statistic = 2.86 c) Ho u = 12 Ha : µ < 12 test statistic = -1.85 %3D p(ZZ-1.85) Pvalue 0.0322 %3D
