If the joint pdf of a two dimensional random variable (X,Y) is given by xy ху 0
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Find the conditional expectations of the given join
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- Suppose that the login times to a computer network follows a Poisson process with an average of 4 logins per minute. Find the probability of exactly 6 logins in 2 minutes.3) Suppose that in the Bay of Fundy, the mean high tide at a particular harbor is 5.4 m above mean sea level with a coefficient of variation of 20% and assume that this is normally distributed. For simplicity, assume that there are two high tides per day and that a year is made up of twelve 30-day months. a) Determine the asymptotic distribution of the monthly maximum tide height at the harbor (ie. specify the form of the distribution and its parameters). b) Using the results of part (a), derive the corresponding distribution for the 50-year maximum tide height and determine the 50-year most probable maximum tide height.3. 3 jobs, with i.i.d. runtimes each U[0, 1], are to be run in parallel on 2 processors. By how much time does the expected flowtime decrease if the schedule is changed from a best fixed schedule to a best schedule with recourse?
- A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 8.2 years. The σ of the population is 2.3 years. At ? = 0.05, can it be concluded that the average age of the taxis in his company is less than the national average?Consider a Qunat vars X and Y and suppose we have collected data on both of them from an underlying population: PowerPoint Slide Show-LinearReg.pptx]-PowerPoint Bivariate Analysis: Modelling a Linear Relation XY After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: Y=f(X)=a+bX b= x1,x2,...,xn У1. Уг...... Уп To that end, we need to estimate a and b. a= nΣ(xy) - ΣxΣy nΣx²-(x)² Σy-bΣx n Ex: Linear of Model of Whr and Salary. Oba 1 2 3 4 E 5 6 7 8 9 10 Whrs Salary Y X 6 8 9 9 10 9 8 7 6 7 8 20 30 35 50 38 25 23 15 26 48 160 270 315 500 342 200 161 90 182 X^2 36 64 81 81 100 81 64 49 36 49 = MULTIPLE CHOICE QUESTION The Cor(X,Y)=0.9, hence b in Y=a+bX is negative negative positive Rewatch Submit5 Calculate XkYk for the n = 5 data points (×₁,Y₁ ) = (2,4), (×2,Y₂) = (3,5), (×3,Y3) = (4,8), (×4,Y4) = (5,10), and k=1 (X5,5) = (6,14). 5 Σ xxYk = [ k=1 (Simplify your answer.)
- 3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.Assume that we collect data (time how late the bus was at the end of the day) in related to following problem. A bus is scheduled to stop at a certain stop every half hour. At the end of the day due to delays that often occur earlier in the day, the bus is likely to be late. The director of the bus line claims that the length of time a bus is late at the end of the day is uniformly distributed and the maximum time that a bus is late is 20 minutes. Assume the lateness of the bus on different days are independent. (a) In a randomly selected day, what is the probability this bus is late more than 5 minutes at the end of the day? If we consider consecutive days, what is the probability that the 6th day will be first (b) day this bus is late more than 5 minutes at the end of the day? What is the probability that at least 10 consecutive days there, before a day with this bus is late more than 5 minutes at the end of the day? (d) . probability that less than 60 of them will be more than 5…Digital communications 2
- Consider two types of call arrivals to a cell in a mobile telephone network: new calls that originate in a cell and calls that are handed over from neighboring cells. It is desirable to give preference to handover calls over new calls. For this reason, some of the channels in the cell are reserved for handover calls, while the rest of the channels are available to both types of calls. = = Suppose that all calls arrive in a cell according to a Poisson process with rate Anc 125 calls per hour for new calls, and λho 50 calls per hour for handover calls. The cell has a capacity of 10 channels. Each call occupies 1 channel and the call time has an exponential distribution with mean two minutes. Suppose that no channels are reserved for handover calls. (a) Calculate the blocking probability in the cell and find the average number of channels used. (b) When a call has to wait, find its average waiting time.23. Find the cumulant generating function of gamma distribution and obtain various cumulants.Solve all plz