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). 1' μ = 1.6, 0² = 0.44 X1 p(x₂) (a) Determine the pmf of T₂ = X₁ + X₂. (b) Calculate кто p(to) = 2.2 2 2 (c) Calculate To = 0.98 HTó OTO 0 = 0.49 0.1 0.01 X 0 How does it relate to μ, the population mean? = 2.2 HT ·μ 1 0.2 2 0.7 1 0.20 X How does it relate to 2, the population variance? 2 X 0.37 2 0.30 3 X 0.09 4 X

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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).
1'
μ = 1.6, 0² = 0.44
X1
p(x₂)
(a) Determine the pmf of T₂ = X₁ + X₂.
(b) Calculate
кто
= 2.2
p(to)
2
2
(c) Calculate To
OTO
OTO
HTó
= 0.98
0
= 0.49
0.1
0.01
X
How does it relate to μ, the population mean?
= 2.2
HT
·μ
0
1
0.2
2
0.7
1
0.20 X
How does it relate to 2, the population variance?
2
X ·0²
0.37
2
0.30
3
X
0.09
4
X
Transcribed Image Text: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). 1' μ = 1.6, 0² = 0.44 X1 p(x₂) (a) Determine the pmf of T₂ = X₁ + X₂. (b) Calculate кто = 2.2 p(to) 2 2 (c) Calculate To OTO OTO HTó = 0.98 0 = 0.49 0.1 0.01 X How does it relate to μ, the population mean? = 2.2 HT ·μ 0 1 0.2 2 0.7 1 0.20 X How does it relate to 2, the population variance? 2 X ·0² 0.37 2 0.30 3 X 0.09 4 X
Expert Solution
Step 1

T0 = X1 + X2 

Sample size (n=2) 

So value of (X1,X2)

(X1,X2) = {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)}

We have T0 = X1 + X2 

So values of T0 

Add values : 

T0 = { 0 , 1, 2, 1, 2, 3, 2, 3, 4 } 

 

P(X1,X2) = P(X1)*P(X2) 

 

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