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

Question

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)

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

   

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)?

what are the values of P(To = 8) and P(To 7)

x1 0 1 2    = 1.1, 2 = 0.89 p(x1)        0.4        0.1        0.5

Explanation / Answer

a) here as P(To) =P(X1=x)*P(X2=To-x)

hence

for P(T=8) =each of X will have 2 lights =0.5*0.5*0.5*0.5=0.0625

P(To>=7) =P(T=7)+P(T=8)=P(3 have 2 lights and one has 1 light+all 4 has 2 lights) =4*0.5*0.5*0.5*0.1+0.5*0.5*0.5*0.5= 0.1125

to 0 1 2 3 4 p(to) 0.16 0.08 0.41 0.1 0.25

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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