Question: 4. Messages arrive to a computer server according to a Poisson distribution with mean rate of 10 per hour. Let X denote the number of

4. Messages arrive to a computer server according to a Poisson distribution with mean rate of 10 per hour. Let X denote the number of messages that arrive to this server per hour. a) Write the probability distribution function of X. (5 points) b) Calculate the expected value and variance of the random variable X. (5 points) c) What is the probability that 1 message will arrive in 1 hour? (5 points) d) What is the probability that 1 message will arrive in 30 minutes? (5 points) Standard Normal Probabilities Table entry for z is the area under the standard normal curve to the left of . 00 02 04 .05 06 07 .08 09 5000 .5160 5199 5239 5279 5319 5359 0.1 .5398 5438 5478 5557 5675 5714 .5793 5832 .5871 5987 -6026 .6064 -6103 0.3 .6179 .6217 .6255 6293 6368 6443 .6480 .6517 .6554 6628 6700 .6736 6808 6844 .6915 .6950 6985 7019 7088 7157 .7190 0.6 7257 7291 7324 7357 .7389 .7422 .7454 7486 7517 .7549 0.7 7580 7611 7673 .7704 .7734 .7764 7794 .7823 7852 7881 7910 7967 .7995 .8023 8078 .8106 0.9 .8159 .8186 8212 .8238 .8264 8289 .8315 .8413 .8438 .8485 .8508 8577 .8599 1.1 .8643 .8686 8749 8790 8810 8830 1.2 .8849 8869 .8888 .8907 .8925 .8944 8980 9015 .9032 9049 .9087 .9099 9115 .9147 .9162 9177 .9192 .9251 9279 .9292 .9306 9319 .9332 9345 .9357 .9382 9394 .9418 9429 .9441 1.6 .9452 .9463 .9474 .9484 .9495 9505 .9515 .9525 .9535 .9545 .9554 .9564 .9573 .9591 .9599 9616 .9625 9633 1.8 .9641 .9649 .9656 .9671 9678 .9693 9699 .9706 1.9 .97 13 .9719 .9726 .9738 .9744 .9756 .9761 .9772 9778 .9793 9798 .9808 9812 9817 2.1 9826 9830 .9838 9842 9850 9854 9857 2.2 .9861 .9864 .9868 .9871 .9875 9878 .9884 9887 9890 2.3 9896 .9898 .9904 .9906 .9909 .9911 9913 9916 2.4 .9918 9920 .9925 .9927 9929 .9932 9934 9936 2.5 .9938 9940 .9941 9943 .9945 9946 .9948 .9949 .9951 9952 .9953 9955 .9957 .9959 .9960 .9961 .9962 2.7 .9963 9964 .9965 .9956 .9967 .9969 .9970 9971 .9972 9973 997 4 2.8 .9974 9975 .9976 9977 .9977 9978 .9979 .9979 .9980 .9981 2.9 .9981 9982 9983 9984 9984 9985 9986 9986 3.0 .9987 .9987 9987 .9988 9988 .9989 9989 .9989 9990 9990 3.1 .9990 .9991 9992 .9993 9993 3.2 .9993 9993 .9994 9994 .9995 9995 3.3 .9996 9996 9996 .9996 .9996 9997 3.4 .9997 9997 9997 9997 9998

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Determine the length of an interval of time such that the probability that no messages arrive...

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. (a) What is the probability that three messages will arrive in 1 hour? (b) What is the...

Jobs arrive at a computer server according to a Poisson process with a rate of 5 jobs per hour. The server can complete one job at a time, and the time that it takes for each job to be completed...

I need the ansure very fast. Question 4) (25 points) Let X(1) represent the number of customers that arrive to a bank in an interval of length t, where ? is measured in hours. Suppose X(/) has a...

Parts arrive according to a Poisson process with mean rate 2 0 per hour. Upon arrival, parts move to a holding vat where they are held until they are moved to a workstation containing two single -...

Records indicate that messages arrive to a computer server following an Exponential distribution at the rate of 8 per hour. 75% of how many messages will arrive between elapses? Question 10 options:...

LAB ACTIVITY #3 For each part of this lab, SUBMIT your solution to everything asked in BOLD RED in Problems 1-6 below. Include the respective R code and output. Part 1 (Continuous Distributions in R)...

LAB ACTIVITY #2 Show your solution to EVERYTHING asked IN RED in Problems 1 - 4 below. Remember to include the relevant R code and output. Part 1 (Continuous Distributions in R) In this part we will...

Find the height h of the pits on a CD (Fig. 25.6a). When the laser beam reflects partly from a pit and partly from land (the flat aluminum surface) on either side of the "pit," the two reflected...

The state of Kansas passed legislation in 2007 that allowed employee to select their employee pay method. The legislation was known as the "paperless payroll law," and many employers opted to give...

Which of the following statements about the market risk of an investment is incorrect? The market risk determines investors' required rate of return A part of the market risk can be eliminated...

August 6,800 $ 630,000 378,000 252,000 September 6,500 $ 682,500 409,500 273,000 Incone Statements For the Three Months Ended September 30 July Sales in units 5,580 Sales $ 577,500 Cost of goods sold...