What would cause our estimate of a bivariate normal distribution to have an inclining slope? When...

What would cause our estimate of a bivariate normal distribution to have an inclining slope? When would the distribution be taller or wider in one axis than another?

Expert Solution

orchestra answered 2 years ago

What is Normal? Give some examples of variables that would have an approximately normal distribution?

n general, when we have a normal distribution, we change it to the standard normal distribution....

n general, when we have a normal distribution, we change it to the standard normal distribution. What is the reason for that?

4.) When would you use the normal distribution? T-distribution? Chi-Square distribution?

Let (X1, X2) have a bivariate normal distribution with mean vector (µ1, µ2), variance σ 12...

Let (X1, X2) have a bivariate normal distribution with mean vector (µ1, µ2), variance σ 12 for X1 and σ 2 2 for X2 and correlation cor(X1, X2) = ρ. (a) Write down the joint density f(x1, x2). (b) Find the marginal distribution f(x1) (c) Find the conditional distribution f(x1 | x2) and the mean and variance of the conditional distribution. (d) Obtain the likelihood equations and calculate the MLE for µ1, µ2, σ12 , σ2 2 , ρ.

Assume that the population of all sister-brother heights has a bivariate normal distribution and that the...

Assume that the population of all sister-brother heights has a bivariate normal distribution and that the data below were sampled from this distribution. Sister height (x) 69 64 65 63 65 62 65 64 66 59 62 Brother height (y) 71 68 66 67 70 71 70 73 72 65 66 Heights of n=11 pairs of siblings (a) Consider the population of all sister-brother heights. Estimate the proportion of all brothers who are at least 5′ 10′′. (b) Suppose that...

Which of the following will cause the IS curve to have a steeper slope? A. An...

Which of the following will cause the IS curve to have a steeper slope? A. An increase in the marginal propensity to consume B. A decrease in the tax rate C. All of these 3 options will D. A decrease in interest rate sensitivity

The annual profits that companies A and B earn follow a normal distribution bivariate. Company A's...

The annual profits that companies A and B earn follow a normal distribution bivariate. Company A's annual profit averages 2000 and standard deviation 1000. Company B has an annual profit with an average of 3000 and a standard deviation of 500. The correlation coefficient between those annual profits is 0.80. Calculate the probability that company B’s annual profit will be lower than 3900, considering that the annual profit of company A is 2300.

Consider a bivariate normal distribution with ?1 = 10, ?2 = 15, ?11 = 2, ?22...

Consider a bivariate normal distribution with ?1 = 10, ?2 = 15, ?11 = 2, ?22 = 3, ?12 = −0.75. Write out the bivariate normal density, ? (?, ?). Round your answers to 3 significant digits I need R code for this question, Thanks

Suppose the random variables X and Y form a bivariate normal distribution. You are given that...

Suppose the random variables X and Y form a bivariate normal distribution. You are given that E[X] = 3, E[Y ] = −2, σX = 4, and σY = 3. Find the probability that X and Y are within 3 of each other under the following additional assumptions: (a) Corr(X, Y ) = 0 (b) Corr(X, Y ) = −0.6

4- In general, when we have a normal distribution, we change it to the standard normal...

4- In general, when we have a normal distribution, we change it to the standard normal distribution. What is the reason for that?

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