from given table:sampling distribution of To is as follows:
x1 | x2 | P(x1,x2) | To |
0 | 0 | 0.0900 | 0 |
1 | 0 | 0.1500 | 1 |
2 | 0 | 0.0600 | 2 |
0 | 1 | 0.1500 | 1 |
1 | 1 | 0.2500 | 2 |
2 | 1 | 0.1000 | 3 |
0 | 2 | 0.0600 | 2 |
1 | 2 | 0.1000 | 3 |
2 | 2 | 0.0400 | 4 |
a)
To | 0 | 1 | 2 | 3 | 4 |
p(To) | 0.09 | 0.3 | 0.37 | 0.2 | 0.04 |
b)
μTo=ΣTo*P(To) = | 1.8000 | |
μTo=2*μ |
c) σTo2 =E(To)2-(E(To))2= | 0.98 | ||
σTo2 =2* σ2 |
d)E(To)=4*μ = | 3.6 | |
V(To)=4*σ2= | 1.96 |
e) P(To=8)=P(all 4 with 2 lights) = | 0.2^4= | 0.0016 | |||
P(T0>=7)=P(To=7)+P(To=8)= | 4*0.2^3*0.5+0.2^4= | 0.0176 |
My Notes 2. -/1 points DevoreStat9 5.E.038 Ask Your Teacher There are two traffic lights on...
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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). 0 1 2 u =...
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