Which of the following could be quantified as a Bernoulli random variable?

a) number of persons in a hospital ward with terminal diagnoses.

b) weights of deliveries at a supermarket.

c) square foot areas of houses being built in a suburban tract development.

d) whether or not employees wear glasses.

e) none of the above.

9. Fifteen percent of the patients seen in a pediatric clinic have a respiratory

complaint. In a Bernoulli process of 10 patients, what is the probability that

at least three have a respiratory complaint?

a) .1298

b) .1798

c) .1960

d) .9453

e) none of the above.

10. Two random variables X and Y have the following properties: x = 10,

?x = 4, y = 8, ?y = 5, ?x,y = ?12.

a) Find the expected value and variance of (3X ? 4Y ).

b) Find the expected value of X2

. (Hint: work from the definition of the

variance of X.)

c) Find the correlation between X and (X + Y )

Just 0.1% of the people in a specific populace have a specific illness (an occurrence pace of .001). Of the individuals who have the sickness, 90% test positive when a specific symptomatic test is applied. Of the individuals who don't have the infection, 90% test negative when the test is applied. Assume that a person from this populace is haphazardly chosen and given the test.

Utilize the overall duplication rule to ascertain P (has sickness AND positive test) and P (no infection AND positive test).

Compute P (positive test) and P (negative test).

Ascertain P (has sickness | positive test). Does the outcome astound you? Give a natural clarification for why this likelihood is little.

For quite a long time, the medication Vioxx, created and

promoted by Merck, was one of the blockbuster

drugs available. One of various

purported Cox-2 mitigating drugs, Vioxx

was considered by numerous individuals a supernatural occurrence drug for

easing the agony from joint inflammation and other difficult

torments. Vioxx was advertised vigorously on TV,

recommended by most doctors, and utilized by an

assessed 2,000,000 Americans.

The entirety of that changed in October 2004, when the

consequences of an enormous report were delivered. The examination,

which followed around 2600 subjects over

a time of around year and a half, reasoned that Vioxx

use throughout an extensive stretch of time caused a huge

expansion in the danger of creating genuine heart

issues. Merck very quickly pulled Vioxx

from the American market and specialists halted

recommending it. Based on the examination, Merck confronted

public humiliation as well as the possibility of

gigantic monetary misfortunes.

All the more explicitly, the investigation had 1287 patients

use Vioxx for a 18-month time span, and it had

another 1299 patients utilize a fake treatment over the equivalent

enough said. Following year and a half, 45 of the Vioxx patients

had created genuine heart issues, though as it were

25 patients on the fake treatment grew such issues.

Given these outcomes, would you concur with the

decision that Vioxx caused a critical increment

in the danger of creating genuine heart issues?

In the first place, answer this from an absolutely measurable mark of

see, where huge methods measurably critical.

What theory should you test, and how might

you run the test? At the point when you run the test, what is

the relating p-esteem? Then, take a gander at it from the

perspective of patients. On the off chance that you were a Vioxx client,

would these outcomes cause you critical concern?

All things considered, a portion of the subjects who took fake treatments

likewise created heart issues, and 45 probably won't be

thought about that amount bigger than 25. At last, look

at it from Merck's perspective. Are the outcomes

essentially important to the organization? What does it

remain to lose? Foster a gauge, regardless of how

wild it very well may be, of the monetary misfortunes Merck may

bring about. Simply think about those American Vioxx clients

also, what they may do.

Atsi shows up at a rail route station at an arbitrary time. It is a speculative world and henceforth prepares show up precisely on schedule and the time between two progressive trains is by and large 10 minutes. Atsi will pause and take the following train that shows up on the station after his appearance. Given that the time that Atsi shows up is consistently irregular and the trains show up 24 hours every day,

1. What is the interim in minutes that Atsi should trust that the following train will show up? What is the dispersion of the holding up season of Atsi?

i23i

2. What is the likelihood that Atsi should stand by in any event 3 additional minutes on the off chance that he has effectively been hanging tight for 6 minutes?

3. In reality, after the appearance of a train, the time until the following train

shows up is a dramatic irregular variable with a mean of 10 minutes. Atsi

shows up at the station not realizing how some time in the past the past train had

come. What is the normal time he should trust that the following train will show up?

What is the appropriation of Atsi's holding up time?

foundation

Karin has attempted to heat for a birthday celebration with a confounded companion. In the companion's kitchen there is preparing for 4 unique sorts of biscuits {M1, ... .. M4}, preparing for 7 diverse arranging glasses {G1, ... , G7}, coconut drops, and game where clover 2 and clover 3 have been traded for hearts 4 and hearts 5 from another deck of cards, two void bundles of 2 and 4 dl that can be utilized as estimating spoons and an enormous three-sided tear dish.

Undertakings

Skopning

For a cluster of biscuit hitter (which would then be able to be seasoned in an unexpected way), 22 dl caster sugar is required.

In what ways would you be able to get this amount of sugar together utilizing the accessible scoops? (We are keen on the number of scoops of every one to take.)

If one somehow managed to make a 10 times as enormous clump, from multiple points of view would the sugar go until it gets together?

While gathering up the sugar, it isn't important to initially utilize one scoop until you are finished with it and afterward proceed with the other. You can change. From multiple points of view can the distinctive scoop numbers in issue 1 be scooped up?15?

On the off chance that, as in the past task, you are keen on how the "scoops" go up to that point, you can put on which you can gather up n dl sugar pleasantly depictions with a recursive number arrangement. Set up a succession that can change the manner in which you gather up n dl of sugar.

Show that your recursive grouping offers a similar response as the computation in issue 3 for 22 dl of sugar.

c. Write the marginal distribution of X in tabular form and verify that it is a proper probability distribution. d. Write the conditional distribution of Y given that X = 1 in tabular form and verify that it is a proper probability distribution..22 Minutes, 50 Seconds 1. Let x and y be random variables with joint cumulative distribution function given by: 0, 3 0 4 x > 4 and y > 3 What is the probability of the event E represented by the blue shaded area in the figure below? 3 2 2:55 PM 40) O 9 4/17/20206) [5 points each] A drawer contains 3 red, 2 green, and 4 blue socks. Two socks are selected at random. Let X denote the number of red socks, and Y denote number of green socks selected. The following table is prepared in order to display the joint probability mass function of X and Y. 0 2 -OIN +3 y a. Show that P(X - 0, Y - 0) - ; and P(X = 1, Y -0) - 1. Give all the details for full credit. Then complete the table. b. Let F denote the joint cumulative distribution function (c.d.f.) of X and Y Compute F(1.0)Question 2 Assume that the joint density function of X and Y is given by / (x, ]) = 1. 0. 1). (b) Find the joint cumulative distribution function F (x. ) of the two random variables. Include all the regions . (c) Find Pur