Question

# Part II Suppose the discrete random variable X has the following probability distribution. x -2 0...

Part II

1. Suppose the discrete random variable X has the following probability distribution.

 x -2 0 2 4 6 P(X=x) 0.09 0.24 0.33 a 0.14

Find the value of a so that this probability distribution is valid. (Sec. 4.3)

1. (Sec. 4.4)
1. Find the mean of the random variable X in Exercise 1 above.

1. Find the variance of the random variable X in Exercise 1 above.

1. Consider the following table for the number of automobiles in Canada in 2005 by vehicle type and fuel type. (Sec. 4.5)

 Light Vehicles Medium Trucks Heavy Trucks Total Gasoline 17,379,447 93,932 3,184 17,476,563 Diesel 541,406 217,210 290,451 1,049,067 Other 72,615 9,493 558 82,666 Total 17,993,468 320,635 294,193 18,608,296

Her Majesty the Queen in Right of Canada (2007). 2005 Canadian Vehicle Survey, Summary Report. Natural Resources Canada’s Office of Energy Efficiency, Ottawa.

1. If a vehicle in 2005 was selected at random, find the probability that it is a light vehicle given that it uses diesel fuel.

1. If a vehicle in 2005 was selected at random, find the probability that it uses gasoline given that it is not a medium truck.

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