6. A bright young economics student at Moscow University in 1950 criticized

the economic policies of the great leader Joseph Stalin. He was arrested and

sentenced to banishment for life to a work camp in the east. In those days

70 percent of those banished were sent to Siberia and 30 percent were sent

to Mongolia. It was widely known that a major difference between Siberia

and Mongolia was that fifty percent of the men in Siberia wore fur hats,

while only 10 percent of the people in Mongolia wore fur hats. The student

was loaded on a railroad box car without windows and shipped east. After58 PROBABILITY

many days the train stopped and he was let out at an unknown location.

As the train pulled away he found himself alone on the prairie with a single

man who would guide him to the work camp where he would spend the rest

of his life. The man was wearing a fur hat. What is the probability he

was in Siberia? In presenting your answer, calculate all joint and marginal

probabilities. Hint: Portray the sample space in rectangular fashion with

location represented along one dimension and whether or not a fur hat is

worn along the other.

Suppose that you take a random sample of 10,000 Americans and find that

1,111 are left- handed. You perform a test of significance to assess whether the

sample data provide evidence that more than 10% of all Americans are lefthanded, and you calculate a test statistic of 3.70 and a p-value of .0001.

Furthermore, you calculate a 99% confidence interval for the proportion of lefthanders in America to be (.103,.119). Consider the following statements: The

sample provides strong evidence that more than 10% of all Americans are lefthanded. The sample provides evidence that the proportion of left-handers in

America is much larger than 10%. Which of these two statements is the more

appropriate conclusion to draw? Explain your answer based on the results of

the significance test and confidence interval.

36. A student wanted to study the ages of couples applying for marriage licenses in

his county. He studied a sample of 94 marriage licenses and found that in 67

cases the husband was older than the wife. Do the sample data provide strong

evidence that the husband is usually older than the wife among couples.

The joint cumulative distribution function of the random variables Y1 and Y2 is given below. Find the joint probability density function and the marginal density functions of these two random variables. F(y1, '2)=1-e OSyISV2 O otherwise. Additional Problem1: Two random variables, X and Y, have joint probability density function given by OSIS1, OSys1 fxY (I, y) = Ary else a) Find the joint cumulative distribution function FxY(I, y) b) Find the probability of the event X c) Find correlation E[XY] d) Find the covariance Cov[X, Y] = E [(X - ux) (Y - MY)] e) Find the correlation coefficient pxY/2. Assume that a random variable X has probability density function f(x) = c+1 8 (2.1) Find the cumulative distribution function of Y = X? + 1. (2.2) Find the probability density function of Y = X2 + 1. 3. Let X and Y be two random variables jointly following the probability density function f(x, y) = (4/9)ry for r E (0, 1) and y e (0, 3). (3.1) Find the joint cumulative distribution function F(x, y). (3.2) Find the conditional density fry(x) of X given Y = y for any specific y E (0, 3).6 of 10 Questions 0:42:24 Question 6 Mark # An insurance company sells automobile liability and collision insurance. Let X denote the percentage of liability policies that will be renewed at the end of their terms and Y the percentage of collision policies that will be renewed at the end of their terms. X and I have the joint cumulative distribution function F(r, v) - n(+y) 0 Sx S 100, 0 Sy SI 2,000,000 Calculate Var(X). 764 833 U 3402 4108 Previous Overview Next