Question

In: Statistics and Probability

At a certain intersection, of all cars traveling north, the relative frequency of cars continuing in...

At a certain intersection, of all cars traveling north, the relative frequency of cars continuing in the same direction is p. The relative frequency of those turning east is q; all others turn west.


Assume that drivers behave independently of one another. A small group of n cars enters the intersection. For this group


(a) What is the marginal distribution of Y, the number of cars turning west? Find the conditional distribution of X, the number of cars turning east, given that Y equals y. Hint: what is the probability that any car not turning west will turn east?
(b) Find the joint distribution of X and Y. Be careful with the limits of validity.

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Allele frequency is the relative frequency of a certain allele type among a certain population. Suppose...
Allele frequency is the relative frequency of a certain allele type among a certain population. Suppose that within a certain area, the allele frequency of A, B and O are 0.2, 0.1, and 0.7, respectively. Suppose that when randomly picking up a person, the first allele type is independent of the second allele type regardless of the type. Calculate the following probabilities: • The probability for this person to have type O blood. • The probability for this person to...
A 1600 kg sedan goes through a wide intersection traveling from north to south when it...
A 1600 kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2000 kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the-scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.750, and the cars slide to a halt at a point 5.30 m west and 6.31 m south of...
A traffic engineer believes that the number of cars passing through a certain intersection between 2...
A traffic engineer believes that the number of cars passing through a certain intersection between 2 and 6 pm on weekdays follows a normal distribution with mean 750 and standard deviation 100. A new highway is opened, and it is hypothesized that the number or cars passing through the intersection should decrease as a result. A sample of 15 weekdays is taken, and the mean number of cars passing through the intersection is 710. Decide whether this reduction in traffic...
Two cars approach an ice-covered intersection. One car, of mass 1.22 103 kg, is initially traveling...
Two cars approach an ice-covered intersection. One car, of mass 1.22 103 kg, is initially traveling north at 10.6 m/s. The other car, of mass 1.66 103 kg, is initially traveling east at 10.6 m/s. The cars reach the intersection at the same instant, collide, and move off coupled together. Find the velocity of the center of mass of the two-car system just after the collision. magnitude direction_______ north of east
State whether a cumulative frequency, relative frequency, relative percent, cumulative relative frequency, or cumulative percent is...
State whether a cumulative frequency, relative frequency, relative percent, cumulative relative frequency, or cumulative percent is most appropriate for describing the following situations. For cumulative distributions, indicate whether these should be summarized from the top down or from bottom up. a. The number of symptoms of stress (ranging between 0 and 12 symptoms) experienced by 180 war veterans. b. The number of calories in school lunches in a sample of 32 local middle schools. c. The number of hours of...
State whether a cumulative frequency, relative frequency, relative percent, cumulative relative frequency, or cumulative percent is...
State whether a cumulative frequency, relative frequency, relative percent, cumulative relative frequency, or cumulative percent is most appropriate for describing the following situations. For cumulative distributions, indicate whether these should be summarized from the top down or from bottom up. a. The frequency of business with at least 20 employees. b. The frequency of college students with less than a 3.0 GPA. c. The percentage of women completing 1, 2, 3, or 4 tasks simultaneously. d. The proportion of pregnancies...
Create frequency table (including  include class interval, frequency, relative frequency and cumulative relative frequency. ) and frequency...
Create frequency table (including  include class interval, frequency, relative frequency and cumulative relative frequency. ) and frequency polygon. Please explain HOW for a thumbs up!! TY 05 06 22 23 34 17 17 26 37 25 17 10 30 06 22 33 06 22 10 27 10 37 13 26 19 27 21 31 22 15 14 28 17 13 28 22 34 17 13 10
Two cars are approaching each other, one traveling north with a momentum of 3 kg-m/s and...
Two cars are approaching each other, one traveling north with a momentum of 3 kg-m/s and one traveling east with a momentum of 4 kg-m/s. The two cars collide and stick together. Right after the collision (choose all that apply) 1. the eastern component of the momentum of the two cars is 4 kg-m/s. 2. the northern component of the momentum of the two cars is 3 kg-m/s. 3. the total momentum of the two cars is 7 kg-m/s
Joe leaves an intersection traveling west in his car. He is 20 feet from the intersection...
Joe leaves an intersection traveling west in his car. He is 20 feet from the intersection 4 seconds later. At the same time, Joshua leaves the intersection heading north in his car so that his position 4 seconds later is 26 feet from the intersection. If, at that instant time, Joe's speed is 8 feet per second and Joshuas' speed is 12 feet per second, find the rate at which the distance between the two cars is changing to the...
police car is traveling south towards the intersection that a robber’s car has just crossed traveling...
police car is traveling south towards the intersection that a robber’s car has just crossed traveling east. The robber’s car is currently traveling 55 mph. The police car’s speed is currently 63 mph. How is the distance between the cars changing when the cop is 1.2 miles from the intersection, and the robber is .5 miles from it? Be sure to answer in a complete sentence. 2. In calm water, an oil spill spreads out in a circular fashion. Suppose...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT