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There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and x, 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 X,, X, is a random sample of size n = 2). X1 1 P(x)0.1 0.3 0.6 H = 1.5, o = 0.45 (a) Determine the pmf of T.= X, + Xg. 1 pt) (b) Calculate T How does it relate to u, the population mean? HT. (c) Calculate oT How does it relate to o, the population variance?

There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and x, 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 X,, X, is a random sample of size n = 2). X1 1 P(x)0.1 0.3 0.6 H = 1.5, o = 0.45 (a) Determine the pmf of T.= X, + Xg. 1 pt) (b) Calculate T How does it relate to u, the population mean? HT. (c) Calculate oT How does it relate to o, the population variance?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, 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 X,, X, is a random sample of size n = 2). X1 1 2 P(x,) 0.1 o.3 0.6 H = 1.5, o2 = 0.45 (a) Determine the pmf of T. = x, + X3. to 1 2 3 p(t) (b) Calculate HT How does it relate to u, the population mean? HT = (c) Calculate o, How does it relate to o, the population variance? 2
Transcribed Image Text:There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, 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 X,, X, is a random sample of size n = 2). X1 1 2 P(x,) 0.1 o.3 0.6 H = 1.5, o2 = 0.45 (a) Determine the pmf of T. = x, + X3. to 1 2 3 p(t) (b) Calculate HT How does it relate to u, the population mean? HT = (c) Calculate o, How does it relate to o, the population variance? 2
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