Question

There are two traffic lights on a commuters 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 frorm 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). μ-09, σ. 0.69 p(%) 0.4 0.3 0.3 (a) Determine the pmf of To = X1 + X2. to p(to) (b) Calculate μΤο. HTO How does it relate to the population mean? (c) Calculated? How does it relate to σ2, the population variance? (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 X/s, what now are the values of E(To) and V(To)? (e) Referring back to (d), what are the values of P(To-8) and P(To 7) [Hint: Dont even thik of listing all possible outcomes!) (Enter your answers to four decimal places.)

0 0
Add a comment Improve this question Transcribed image text
Answer #1

a)

t0     P(t0)

0    P(X1 = 0) * P(X2 = 0) = 0.4 * 0.4 = 0.16

1    2 * P(X1 = 0) * P(X2 = 1) = 2 * 0.4 * 0.3 = 0.24

2    2 * P(X1 = 0) * P(X2 = 2) + P(X1 = 1) * P(X2 = 1) = 2 * 0.4 * 0.3 + 0.3 * 0.3 = 0.33

3    2 * P(X1 = 1) * P(X2 = 2) = 2 * 0.3 * 0.3 = 0.18

4    P(X1 = 2) * P(X2 = 2) = 0.3 * 0.3 = 0.09

b) µT0 = 0 * 0.16 + 1 * 0.24 + 2 * 0.33 + 3 * 0.18 + 4 * 0.09 = 1.8

µT0 = 2 * µ

c) E(X2) = 02 * 0.16 + 12 * 0.24 + 22 * 0.33 + 32 * 0.18 + 42 * 0.09 = 4.62

\sigma_{t_{0}}^2 = E(X2) - (E(X))2 = 4.62 - 1.82 = 1.38

\sigma_{t_{0}}^2=2*\sigma^2

d) T0 = X1 + X2 + X3 + X4

E(T0) = 4 * 0.9 = 3.6

V(T0) = 4 * 0.69 = 2.76

e) P(T0 = 8) = P(X1 = 2) * P(X2 = 2) * P(X3 = 2) * P(X4 = 2) = 0.3 * 0.3 * 0.3 * 0.3 = 0.0081

P(T0> 7) = P(T0 = 7) + P(T0 = 8)

               = 4 * 0.3 * 0.3 * 0.3 * 0.3 + 0.0081

               = 0.0405

Add a comment
Know the answer?
Add Answer to:
There are two traffic lights on a commuter's route to and from work. Let X1 be...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

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
  • 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). = 0.9,02 = 0.69 x1 0 1...

  • 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). 0 1 2 u =...

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

    There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, 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 X, X, is a random sample of size n = 2). X1 u =0.9,02 = 0.49...

  • There are two traffic llghts n a commuter's route to and from work. Let X he...

    There are two traffic llghts n a commuter's route to and from work. Let X he the number of lights at whlch the commuter must stop on hls way to work, and X2 he 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 (soX, X is a random sample of size n-2). μ-1.3, σ2-0.61 p(x1) 0.2 0.3 0.S (a) Determine...

  • 38. There are two traffic lights on a commuter's route to and from work. Let Xi...

    38. There are two traffic lights on a commuter's route to and from work. Let Xi 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 these two variables are independent, each with pmf given in the accompanying table (so X, Xy is a random sample of size a a. Determine the pemf of T,X b. Calculate...

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

    There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, 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 X,, X, is a random sample of size n 2) 1 2 1.5, -0.65 0.2 0.1...

  • 38. There are two traffic lights on a commuter's route to and from work. Let Xi...

    38. There are two traffic lights on a commuter's route to and from work. Let Xi 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 these two variables are independent each with penf given in the acompanying table so X, X2 is a rand om sample of sue d. Let Χ, and x, be the number...

  • 2. 1 points DevoreStats 5.E.038. My Notes Ask Your Teacher There are two traffic lights on a commuter's route to an...

    2. 1 points DevoreStats 5.E.038. My Notes Ask Your Teacher 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 X2, X2 is a random sample...

  • My Notes 2. -/1 points DevoreStat9 5.E.038 Ask Your Teacher There are two traffic lights on...

    My Notes 2. -/1 points DevoreStat9 5.E.038 Ask Your Teacher 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 X, x2 is a random sample...

  • 38. There are two traffic lights on a commuters route to and from work. Let Xi...

    38. There are two traffic lights on a commuters route to and from work. Let Xi 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 these two variables are independent, each with pmf given in the accompanying table (so Xj, X is a random sample of size n-2). d. Let XI and X. be the number...

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
ADVERTISEMENT