Xí,..., Xn are independent Poisson random variables with mean \, Find UMVUE for 2.

Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter ? = 20  What is the probability that the number of drivers will be at most 19? What is the probability that the number of drivers will exceed 29? What is the probability that the number of drivers will be between 19 and 29, inclusive?

The number of fish that a person catches per hourat Woods Canyon Lake is a random variable having the Poisson distribution with λ = 1.6. What are the probabil-ities that a person fishing there will catch (a) four fish in 2 hours;(b) at least two fish in 3 hours;(c) at most three fish in 4 hours?

PLEASE DRAW THE BELL CURVE OF THE RESULTS OF THESE TWO!!! ONLY BELL CURVE

An automobile manufacturer has developed a new type of bumper, which is supposed to absorb impacts with less damage than previous bumpers. The manufacturer has used this bumper in a sequence of 25 controlled crashes against a wall, each at 10 mph, using one of its compact car models. Let X = the number of crashes that result in no visible damage to the automobile.   1.The (parameter/random_variable/statistics/variable)  , [variable],[statistics],[random_variable] to be estimated is p. 2. Continuing this question, p the is (percentage/median/average/poportion) of such crushes that result in no damage [alternatively, p = P(no damage in a single crash)]. Select the correct answer from the options inside the (bracket).

The number of major faults on a randomly chosen 1 km stretch of highway has a Poisson distribution with mean 1.7. The random variable X is the distance (in km) between two successive major faults on the highway. Part a) What is the probability of having at least one major fault in the next 2 km stretch on the highway? Give your answer to 3 decimal places. Part b) Which of the following describes the distribution of X, the distance between two successive major faults on the highway? OA. X - Exponential(mean OB. X - Exponential(mean = 2 - 1.7) Oc. X - Exponential(mean = 217) OD. X - Poisson(2 - 1.7) OE. X- Poisson(1.7) (푸 Part c) What is the mean distance (in km) and standard deviation between successive major faults? OA. mean = 3.4000; standard deviation = 3.4000 OB. mean = 0.5882; standard deviation = 0.5882 OC. mean = 0.2941; standard deviation = 0.2941 OD. mean = 0.5882; standard deviation = 0.3460 O E. mean = 1.7; standard deviation = 1.7 Part d) What is the median distance (in km)…

The amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 20 minutes and a standaard deviation of 7 mintuses. Find the probability that a randomly selected athlete uses a stairclimber for​ (a) less than 15 minutes (b) between 20 and 27 minutes and​ (c) more than 30 minutes  (a) The probability that a randomly selected athlete uses a stairclimber for less than 15 minutes is ( round to four decimal places as needed )