o Chapters 5b and 6 There are two traffic lights on a commuter\'s route to and f

Question

o Chapters 5b and 6 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 xa be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the given in the accompanying table (so is a random sample of size n 2). 1.3, o2-0.41. POxh) 0.1 0.5 0.4 (a) Determine the pmf of To X1 +X2. (b) Calculate RT. How does it relate to H, the population mean? How does it relate to o2, 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(To) VITo) (e) Referring back to (d), what are the values of POT 8) and P(To z 7) [Hint: Don't even think of listing all possible outcomest (Enter your answers to four decimal 1

Explanation / Answer

a)

b) µto = to*p(to) = 0*0.01 + 0.1*1 + 0.33*2 + 0.4*3 + 0.16*4 = 2.6
µto = 2*µ

c) to2 = (to - µto)2*p(to) = (0-2.6)2*0.01 + (1-2.6)2*0.1 + (2-2.6)2*0.33 + (3-2.6)2*0.4 + (4-2.6)2*0.16 = 0.82
to2 = 2*2

d) We found the relations in the previous problem.
E(T0) = 2*µto = 2*2.6 = 5.2
V(T0) = 2*to2 = 2*0.82 = 1.64

e)P(To = 8) = P( 2 on all four traffic lights) = 0.4*0.4*0.4*0.4 = 0.0256

P(To >=7) = P(To = 7) + P(To = 8)
P(To = 7)
P(1 on the first traffic light and 2 on the remaining 3 lights) = 0.5*0.4*0.4*0.4 = 0.032

This can happen 4 ways, therefore P(To = 7) = 4*0.032 = 0.128

P(To>=7) = 0.128+0.0256 = 0.1536

to     0     1    2    3    4 p(to)   0.01     .1   .33    .4     .16

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.