The joint probability distribution of two random variables X and Y is given in the following table.
1. Calculate the marginal probability distribution of X.
2. Calculate the marginal probability distribution of Y.
3. Calculate E( X ) and s.d.( X ).
4. Calculate E( Y ) and s.d.( Y )
5. Calculate cov(X, Y) and corr(X, Y).
6. Calculate the conditional probability distribution of X given Y = -1.
7. Calculate the conditional probability distribution of X given Y = 2.
8. Calculate E( X | Y = -1 ) and var( X | Y = -1 ).
9. Calculate E( X | Y = 2 ) and var( X | Y = 2 ).
10. Verify the Law of Iterated Expectations E(X)=E[E(X|Y)] by using your previous results.
11. Are X and Y independent random variables? Justify your answer based on answers to the preceding questions.
More cereal. In Exercise 37 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces. a) Find the expected amount of cereal left in the box. b) What’s the standard deviation? c) If the weight of the remaining cereal can be described by a Normal model, what’s the probability that the box still contains more than 13 ounces?
70% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 31 owned dogs are randomly selected, find the probability that
a. Exactly 20 of them are spayed or neutered.
b. At most 24 of them are spayed or neutered.
c. At least 22 of them are spayed or neutered.
d. Between 16 and 23 (including 16 and 23) of them are spayed or neutered.
Round all answers to 4 decimal places.
In a loan database, there are 11 loans to clients with 19 years of business experience. Also, there are 77 loans made to clients with a College education. In the database there are 82 loans to clients with 19 years of experience or who have a College education. How many loans were made to clients with a College education who also had 19 years of experience?
1. Random sample of size 4 are drawn from the finite population which consists of the numbers 2,3,7,8,and 10. a. What is the population mean, population variance and population standard deviation of the given data? b. What is the sampling distribution of the sample means for a sample of size 2 which can be drawn without replacement from the given population? c. What is the mean, variance and standard deviation of the samp
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