Question

In: Statistics and Probability

There are two traffic lights on a commuter's route to and from work. Let X1 be...

There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2).

x1 0 1 2 μ = 1.2, σ2 = 0.76
p(x1)     0.3     0.2     0.5  

(a) Determine the pmf of To = X1 + X2.

to 0 1 2 3 4
p(to)                         


(b) Calculate μTo.
μTo =

How does it relate to μ, the population mean?
μTo =  · μ

(c) Calculate σTo2.

σTo2 =


How does it relate to σ2, the population variance?
σTo2 =  · σ2

(d) Let X3 and X4 be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With To = the sum of all four Xi's, what now are the values of E(To) and V(To)?

E(To) =
V(To) =


(e) Referring back to (d), what are the values of

P(To = 8) and P(To ≥ 7)

[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)

P(To = 8)

=

P(To ≥ 7)

=

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 μ...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning home from work. Suppose these two variables are independent, each with pmf given in the accompanying table. (so X1, X2 is a random sample size n=2.) x1 = 0 1 2 p(x1)= .2 .5 .3...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 p(x1)...
There are two traffic lights on a commuter's route to and from work. Let X1 be...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 μ...
There are two traffic lights on the route used by a certain individual to go from...
There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.5, P(F) = 0.3, and P(E ∩ F) = 0.12. (a) What is the probability that the individual must stop at at least one light; that is, what is the...
5. A driver encounters two traffic lights on the way to work each morning. Each light...
5. A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinations of colors is given in the following table: Second Light First Light R Y G R 0.31 0.02 0.18 Y 0.02 0.03 0.03 G 0.14 0.04 0.23 a) What is the probability that the first light is red? b) What is the probability that the second light is green? c) Find the...
A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the...
A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the way to work each day. Over a period of time, the following pattern has emerged: - Each day the first light is green - If a light is green, then the next one is always red - If he encounters a green light and then a red one, then the next will be green with probability 0.6 and red with probability .4. - If...
A commuter must pass through five traffic lights on her way to work and will have...
A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below: x 0 1 2 3 4 5 p(x) 0.04 0.23 p 0.1 0.1 0.1 a)Find the probability that she hits at most 3 red lights. Answer to 2 decimal places. b)Find the probability that she hits at least 3...
A commuter must pass through five traffic lights on her way to work and will have...
A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below: x 0 1 2 3 4 5 p(x) 0.03 0.21 p 0.1 0.1 0.05 Find the probability that she hits at most 3 red lights. Answer to 2 decimal places. Tries 0/5 Find the probability that she hits at...
During our morning commute we encounter two traffic lights which are distant from one another and...
During our morning commute we encounter two traffic lights which are distant from one another and may be assumed to operate independently. There is a 50% chance that we will have to stop at the first of the lights, and there is a 30% chance that we’ll be stopped by the second light. Find the probability that we are stopped by at least one of the lights
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT