MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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If fruit flies are randomly distributed throughout the neighborhood, then the number of fruit flies per trap should follow a poisson distribution. Use the sample
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- Suppose we take a sample of size 30 from a geometrical distribution 200 times. Draw a graph of the distribution of X¯n, this is a histogram of 200 values of the sample mean. Calculate the expected value and variance of X¯n. How is X¯ n distributed - name the distribution. Use an important theorem. Do it in R commander.arrow_forwardThe number of calls received by an office follows Poisson distribution with a mean of 8 calls. What is the probability of receiving 5 calls in a day?arrow_forwardThe number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter ?y for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?arrow_forward
- A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Y1 = 0, if the policy holder does not have any health issues; Y1 = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).arrow_forwardThe number of corner kicks in a 90 minute soccer game follows a Poisson distribution with a mean of 5. Then, the probability that there will be 3 corner kicks in 45 minutes isarrow_forwardThe number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page. What is the probability that the typist makes 3 errors on a page? What is the probability that a randomly selected page does not need to be retyped?arrow_forward
- The number of goals scored at state college hockey games follows as poisson distribution with a mean of five goals per game. Find the probability that a randomly selected state college hockey game would have more than three goalsarrow_forwardA certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.arrow_forwardConsider a Poisson distribution with an average of 4 customers per minute at the local grocery store. If X = the number of arrivals per minute:Find the probability of 8 customers or less arriving within a minute. Find the probability of more than 7 customers arriving within a minute. Find the probability of 3 customers arriving within a minute.arrow_forward
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