Determine the value of c and the covariance and correlation for the joint probability mass function f(x, y) = c(x + y) for x = 1, 2, 3 and y = 1, 2, 3.

In a certain game it is possible to win either 1,2,3,4, or 5 dollars. The probability of winning d dollars is proportional to 1/d.

(a) What is the probability of winning d dollars (d ∈{1,2,3,4,5})?

(b) Would you play this game for $4? What about for $3? Hint. You must calculate the expected value for this problem!

(c) What is the variance of the expected winnings of this game?

Select ALL of the probability comparisons that can be used to determine if gender and whether a person dies are independent.

Group of answer choices

a. Compare P(died|female) to P(died)

b. Compare P(died|male) to P(died)

c. Compare P(female AND died) to P(female)P(died)

d. Compare P(male AND died) to P(male)P(died)

e. Compare P(female AND died) to P(male AND died)

f. Compare P(female) to P(died)

1. What is the probability that out of a class of 25 people at least two have the same birthday? Assume that each birthday is equally likely and that there are only 365 days on which to be born each year. State you answer as a decimal rounded to six decimal places.

What is the probability that out of four people, no two were born on the same day of the week?

According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze. ​(​a) What is the probability that among 10 randomly observed individuals exactly 7 do not cover their mouth when​ sneezing? ​(​b) What is the probability that among 10 randomly observed individuals fewer than 4 do not cover their mouth when​ sneezing? ​(​c) Would you be surprised​ if, after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing? Why?

Give a formal statement of the following models identifying the probability laws of the data and the parameter space.

i.A measuring instrument is being used to obtain n independent determinations of a physical constant µ. Suppose that the measuring instrument is known to be biased to the positive side by 0.1 units. Assume that the errors are otherwise identically distributed normal random variables with known variance.

ii.suppose that the amount of bias is positive but unknown. Can you perceive any difficulties in making statements about µ for this model?

Determine the probability that in a group of 5 people, at least two share the same birth month. Assume that all 12 months are equally likely to be someone’s birth month.

a) How many choices are there for the birth months of these 5 people (without any restrictions)?

b) How many choices are there for the 5 people to have all different birth months?

c) Report the probability that in a group of 5 people, at least two share the same birth month. (Report your final answer as a decimal, as well as showing how you reach that answer.)

d) Is it reasonable to assume that the 12 months of the year are equally likely to be a person’s birth month? Explain briefly.

Given the data in the spreadsheet below, what is the probability of completing the critical path of the project in 34 or more time units?