There are two traffic lights on my way to work. Let X 1 be the number of lights

Q: There are two traffic lights on my way to work. Let X 1 be the number of lights

a) as P(To)=P(X1)*P(X2) therefore below is probability distribution: b)?To =3.0 ?To =2 *? c) ?To2 =0.90 ?To2 =2* ?2 To 0 1 2 3 4 p(To) 0.01 0.06 0.21 0.36 0.36

ID: 3371746 • Letter: T

Question

There are two traffic lights on my way to work. Let X1 be the number of lights at which I must stop, and suppose that the distribution of X1 is as follows.

Let X2 be the number of lights at which I must stop on the way home; X2 is independent of X1. Assume that X2 has the same distribution as X1, so that X1, X2 is a random sample of size n = 2.

(a) Let To = X1 + X2, and determine the probability distribution of To.

(b) Calculate ?To.

How does it relate to ?, the population mean?
?To = ____________________ · ?

How does it relate to ?2, the population variance?
?To2 = __________________ · ?2

2 ?-1.5, ?2-0.45 51, 0 p(xi) 0.1 0.3 0.6

Explanation / Answer

as P(To)=P(X1)*P(X2)

therefore below is probability distribution:

b)?To =3.0

?To =2 *?

c) ?To2 =0.90

?To2 =2* ?2

To 0 1 2 3 4 p(To) 0.01 0.06 0.21 0.36 0.36

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There are two traffic lights on my way to work. Let X 1 be the number of lights

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