HomeworkLib
Question

2. The number of cars passing through each lane of a toll booth per minute is represented by a random variable, C, and the number of trucks passing through it is represented by another random variable, T. During the morning peak hour, the joint probability mass function of C and T is given by the following table 0 0.05 0.08 0.08 1 0.05 0.09 0.11 0.08 0.22 0.11 0.06 0.05 0.02 Find the marginal probability mass function of T, pr(t) b. Find Hc and oc c. Find Cov(T, C) and pTC d. Find the conditional probability mass function pcIr(c12) a. If the toll per car is $2 and the toll per truck is $3 then find the mean and standard deviation of the total amount of toll paid by the vehicles passing through the toll booth per lane per minute e. f. Find the probability that the toll collected in a randomly chosen minute for a randomly chosen lane is exactly $6

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

3 0 08 d 0 22 oOS 2 0,08 o.11 σf] 0.02. a) Merginu] pmf of T o-osto-os to-osto,06 fr(2)-o 32 ㄒㄧ -0-T-1 2 0:1013 2 eO+0.25+0.82 +0/39ニo(0,21) ti(02s)+5 (041) tg@/3) EC2): 3.06 ニ0(0.24 ) +1(ass ) +4(132 ) 12. 11(1) Co.09) 4-1(2)(022) + ↓ (3) (G.Os)+2 (o)(0.02) +20 )(1)2(2)(0 11 )203 002 )

0 0
Add a comment
Know the answer?
Add Answer to:
2. The number of cars passing through each lane of a toll booth per minute is...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 3.25. Suppose45%ofthecarsontheroadaredomesticbrandsand55%areforeign brands. Let N.t/ be the number of cars crossing at a given toll booth...

    3.25. Suppose45%ofthecarsontheroadaredomesticbrandsand55%areforeign brands. Let N.t/ be the number of cars crossing at a given toll booth during .0;t?. Suppose fN.t/;t ? 0g is a PP with rate 40 per minute. (1)What is the probability that four foreign cars and five domestic cars cross the intersection during a 10-second interval? (2)In Computational Problem 3.25, suppose 30 foreign cars have crossed the toll booth during a 1-minute interval. What is the expected number of domestic cars that cross the intersection during this...

  • 2. The number of cars passing through a road in 1 minute follows a Poisson Distribution...

    2. The number of cars passing through a road in 1 minute follows a Poisson Distribution with mean 5. (a) Find the probability that there are 2 cars passing through the road in one minute. (3 marks) (b) Find the probability that there are 4 cars passing through the road in two minutes. (3 marks) (c) Find the probability that there are 4 cars passing through the road in two minutes given that there are 2 cars passing through the...

  • The average number of cars per hour arriving at a toll booth is 57 while the...

    The average number of cars per hour arriving at a toll booth is 57 while the standard deviation is 15. (a) Use Markov’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour. (b) Use Chebyshev’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour

  • The number of cars passing through the M50 toll follows a Poisson distribution with a rate...

    The number of cars passing through the M50 toll follows a Poisson distribution with a rate of lambda = 90000 cars per day. What is the probability that more than 187950 euro is collected in tolls on a given day? (correct to 4 decimal places)

  • The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded....

    The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a 15-minute period 25 27 25 28 28 25 30 27 35 31 31 29 24 31 25 20 15 27 27 27 O A. 31 vehicles OB. 28 vehicles O c. 26 85 vehicles OD. 27 vehicles Click to select your answer PrtScn. Home in

  • B 6.4.5-T 125 beats per minute. Complete parts (a) through below Assume that females have pulse...

    B 6.4.5-T 125 beats per minute. Complete parts (a) through below Assume that females have pulse rates that are normally distributed with a mean of 75.0 beats per minute and a standard deviation of a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute The probability is (Round to four decimal places as needed.) CA Enter your answer in the answer box and then click Check Answer 2...

  • The number of automobiles entering a tunnel per 2-minute period follows a Poisson distribution. The mean...

    The number of automobiles entering a tunnel per 2-minute period follows a Poisson distribution. The mean number of automobiles entering a tunnel per 2-minute period is four. (A) Find the probability that the number of automobiles entering the tunnel during a 2minute period exceeds one. (B) Assume that the tunnel is observed during four 2-minute intervals, thus giving 4 independent observations, X1, X2, X3, X4, on a Poisson random variable. Find the probability that the number of automobiles entering the...

  • 4. The number of claims per week at an Suppose that Y has probability mass function...

    4. The number of claims per week at an Suppose that Y has probability mass function insurance company is a random variable Y Pr(v),0,1,2. py(y) 0, otherwise. The moment generating function (mgf) of Y is given by my(t)-c(1-e2)- for values of t<2. You do not need to prove this. (a) Show that c1-2 (b) What is the probability that there are at least 2 claims in a given week? (c) Find E(Y)

  • Suppose the number of patients per week that visit a health center follows a Poisson distribution...

    Suppose the number of patients per week that visit a health center follows a Poisson distribution with a rate of 300 patients per week. Let the random variable X count the number of patients per week that visit the health center. A) State the distribution of the random variable defined above B) Compute the probability that during a randomly selected week exactly 280 patients visit the health care center C) Compute the probability that during a randomly selected week at...

  • Part C. 5.4.5-T 760 beats per minute and a standard deviation of a 125 beats per...

    Part C. 5.4.5-T 760 beats per minute and a standard deviation of a 125 beats per minuto Complete parts (a Assume that females have pulse rates that are normally distributed with a mean of through (c) bolow b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 boats per minute The probability is 0.8315 (Round to four decimal places as needed) c. Why can the normal distribution be...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT