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- 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 probability1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given monthsd) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X = 2).
- Consider a Poisson distribution with u = 4.6 Compute f(2) (ANSWER MUST BE 4 DIGITS)Let X1, X2,..Xn be a random sample from a Poisson distribution with variance 0. Find the UMVUE for Pe(X=0). R(Ctrl) -If the number X of particles emitted during a 1-h period from a radioactive source has a Poisson distribution with parameter 2 = 4 and that the probability that any emitted particle is recorded is p = 0.9, find the probability distribution of the number Y of the particles recorded in a 1-h period and hence the probability that no particle is recorded.
- 3 a. Let X have a Poisson distribution with a mean of 3. Define Y = (X-3) ^2 , specify pdf from Y.b. Let Y have a Poisson distribution with a mean of 5. Define Y=Z+X where Z and X are independent, where X is a random variable at point a, determine the distribution and pdf of Z.The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time. Suppose the number X, of students walking out the 11th Avenue door of JJC in any one-hour period can be modeled as a Poisson random variable with parameter i = 5. Let Y be the number of students walking out the 11th Avenue door of JJC in any two-hour period. Y can also be modeled as a Poisson random variable. . a. For our model, what is expected value of X? b. What is the probability that X = 4? c. What is the probability that X 4 e. What is the probability that X = 9 f. Y also has a Poisson distribution. What is the parameter Ay for Y? g. What is variance of X? h. What is the standard deviation of X? i. What is the probability that Y = 9 j. What is the probability that Y < 9?Q11. Let X1,X 2,.,X, be a random sample from a Poisson distribution with parameter 2. (a) Find the Cramer-Rao lower bound for the variance of any unbiased estimator of 1. (b) Find the maximum likelihood estimator (m.l.e.) of å. (c) Is this m.l.e. unbiased and does its variance attain the Cramer-Rao lower bound?
