Please submit only correct and detailed answers! Otherwise don't attempt!

Data was taken on height and weight from the entire population of 700 mountain gorillas living in the Democratic Republic of Congo:

ht\wt light average heavy

Short 170 70 30

Tall 85 190 155

Let X encode the weight, taking the values of a randomly chosen gorilla: 0, 1, 2 for light, average, and heavy respectively.

Likewise, let Y encode the height, taking values 0 and 1 for short and tall respectively.

(a) Determine the joint pmf of X and Y and the marginal pmf's of X and of Y.

(b) Are X and Y independent?

(c) Find the covariance of X and Y.

For this part, you need a numerical (no variables) expression, but you can leave it unevaluated.

(d) Find the correlation of X and Y.

(d) The definition of correlation is Cor(X, Y) = Cov(X, Y )/ XY

compute the variances of X and Y .

In the ancient days, the skull was believed less developed. With time there have been tremendous steps in the generation of advanced cranium and the mid brain components to cater for the modern man. In order to shed more light on such a topic, answer the following questions as required

additional case study;

Intelligence is instead more strongly linked to the brain sizerelative to the body size. If a large brain is housed in a small body, there is less low-level signal processing and control that the brain has to carry out. As a result, the brain can be freed up for more higher-order thinking. But even this picture is over-simplified. Intelligence seems to depend on many things: absolute brain size, relative brain size, connectivity, energy expenditure, etc. But as a rough model, relative brain size is indeed correlated to intelligence within main groups of organisms. While humans do not have the biggest brains overall, we do have thebiggest brains relative to our body sizeamong the mammals.

Questions;

1. Elaborate on the weight of the brain that render it normal for effective psychological functioning

2. Locate the brain topographically

3. Propose the reduced part of the brain as exposed by the mid brain

4. Which foramen is paired in mammalian brain?explain

5. locate/position the Roof of diencephalon and explain

6. What is the relationship between the Corpora Quadrigeminaand the colliculi- two inferior

7. Is it true to state the Optic lobes control visual reflexes?why/why not?

8. Propose of the pairs of the non absenteeism of the optic lobes

9. mid brain is formed of ___________ parts.explain

10. Synonymies the midbrain with explanation