Two teams A and B play a soccer match. The number of goals scored by Team A is modeled by aPoisson process N₁ (t) with rate X₁ = 0.02 goals per minute, and the number of goals scored byTeam B is modeled by a Poisson process N₂ (t) with rate A₂ = 0.03 goals per minute. The twoprocesses are assumed to be independent. Let N(t) be the total number of goals in the game upto and including time t. The game lasts for 90 minutes.a. Find the probability that no goals are scored, i.e., the game ends with a 0-0 draw.b. Find the probability that at least two goals are scored in the game.c. Find the probability of the final score beingTeam A: 1, Team B: 2d. Find the probability that they draw.

It is given that two teams A and B play a soccer match.The number of goals scored by team A is…

Answered: Two teams A and B play a soccer match.…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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+. A nuclear power facility produces a vast amount of heat, which is usually discharged into aquatic systems. This heat raises the temperature of the aquatic system, resulting in a greater concentration of chlorophyll a, which in turn extends the growing season. To study this effect, water samples were collected monthly at 3 stations for a period of 12 months. Station A is located closest to a potential heated water discharge, station C is located farthest away from the discharge, and station B is located halfway between stations A and C. The following concentrations of chlorophyll a were recorded. Station Month A B C January February March 9.867 3.723 4.410 14.035 8.416 11.100 10.700 20.723 4.470 April Мay June 13.853 9.168 8.010 7.067 4.778 34.080 9.145 11.670 8.990 July August September October November December 7.357 8.463 3.350 3.358 4.086 4.500 4.210 4.233 6.830 3.630 2.320 5.800 2.953 3.843 3.480 2.640 3.610 3.020 Perform an analysis of variance and test the hypothesis, at the…
ARCH(1) model o? = w+ ae?_1. Define Y; = e? and u: = e? – o?. %3D Show that Y, can be written as a specific autoregressive process with innovation u.
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Vehicles arrive at a car detailing service at a rate of 10 per minute according to a Poissondistribution. For simplicity, assume that there is only one lane and one worker who can serve atan average rate of 12 vehicles per minute. Service times are exponentially distributed. Part A: What is the average length of the queue? Part B: What is the average time a vehicle must spend to get through the system? Part C: What is the utilization rate of the worker? Part D: What is the probability that when you arrive at the shop, there will be three ormore vehicles ahead of you?
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lecture(12.11A): Researchers were interested in the effects of co-sleeping on nightime waking and crying in infants. .They assesed the number of minutes parents reported that their infants were awake and crying for a period of three days. Five of the infants co-slept with thier mothers(Co) and four infants slept in crib(Cr).The researchers wanted to see if there was a difference in the total number of minutes of crying during the 3 nights. for the two groups. A summary of the data is given below Co-sleepers night time crying in minutes: 8, 4, 7, 7, 6 Crib-sleepers night time crying in minutes: 30, 17, 22, 25 Test the hypotheses at (aplha=.05) level of signifcance. using the 5 step hypotheses testing procedure. Clealy state the null and alternative hypotheses. Round your answer to 2 decimal places.
A Random process X(t) is applied to a network with impulse response h(t) = u(t) exp (-bt) where b > 0 is a constant. The cross- correlation of X(t) with the output Y(t) is known to have the same form, Ryy(t) = u(t)t exp(-bt) (i) Find the auto-correlation of Y(t).
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