This post provides practice problems to reinforce the concept of bivariate normal distribution discussed in two posts – one is a detailed introduction to bivariate normal distribution and the other is a further discussion that brings out more mathematical properties of the bivariate normal distribution. The properties discussed in these two posts form the basis for the calculation behind the practice problems presented here.
The practice problems presented here are mostly on calculating probabilities. The normal probabilities can be obtained using a normal table or a calculator that has a function for normal distribution (such as TI84+). The answers for normal probabilities given at the end of the post have two versions – one using a normal table (found here) and the other one using TI84+.
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Practice Problem 5A 
Suppose that and follow a bivariate normal distribution with parameters , , , and . Determine the following.

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Practice Problem 5B 
Suppose that and follow a bivariate normal distribution with parameters , , , and . Determine the following.

Practice Problem 5C 
Let and have a bivariate normal distribution with parameters , , , and . Determine the following.

Practice Problem 5D 
Suppose is the height (in inches) and is the weight (in pounds) of a male student in a large university. Furthermore suppose that and follow a bivariate normal distribution with parameters , , , and .

Practice Problem 5E 
Suppose that and have a bivariate normal distribution with parameters , , , and .
Further suppose that . Determine . 
Practice Problem 5F 
Suppose that and have a bivariate normal distribution with parameters , , , and .

Practice Problem 5G 
Let and have a bivariate normal distribution with parameters , , , and . Determine the following.

Practice Problem 5H 
Let and have a bivariate normal distribution with parameters , , , and . Determine the following probabilities.

Practice Problem 5I 
For a couple from a large population of married couples, let be the height (in inches) of the husband and let be the height (in inches) of the wife. Suppose that and have a bivriate normal distribution with parameters , , , and .

Practice Problem 5J 
The annual revenues of Company X and Company Y are positively correlated since the correlation coefficient between the two revenues is 0.65. The annual revenue of Company X is, on average, 4,500 with standard deviation 1,500. The annual revenue of Company Y is, on average, 5,500 with standard deviation 2,000.

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Problem  ………..Answer 

5A 

5B 

5C 

5D 

5E 

5F 

5G 

5H 

5I 

5J 

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