The probability of winning a stake is $5. The chance of winning each stake is 50%. You plan to bet in increments of $5, $10, $20, $40, $80, $160 ($315 in total) for each consecutive loss. For each win, you start back at $5 and continue betting following the incremental bet scheme. This means you would need to win 64 times without losing 7 in a row. What is the probability of this happening?

6. A standard drug is used to treat a certain disease. The probability with which the drug is effective is 0.85. A new drug is developed and it is desired to determine if the new drug performs better than the standard. An experiment was conducted with which 300 people are given the new drug.

a. State symbolically the null and alternative hypotheses.

b. What is the critical value and rejection region of the proposed test?

c. If in fact, the success rate of the drug is 0.9, what is the power of the test?

d. When the experiment was actually carried out, it was found that the new drug was effective in 269 of the patients. Find the p-value of the test.

statistics, probability and Fourier series its application in the oil and gas industry

There are three securities in the market. The following chart shows their possible payoffs:

a-1. What is the expected return of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

a-2. What is the standard deviation of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b-1. What are the covariances between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 5 decimal places, e.g., 32.16162.)

b-2. What are the correlations between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

c-1. What is the expected return of a portfolio with half of its funds invested in Security 1 and half in Security 2? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c-2. What is the standard deviation of a portfolio with half of its funds invested in Security 1 and half in Security 2? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

d-1. What is the expected return of a portfolio with half of its funds invested in Security 1 and half in Security 3? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

d-2. What is the standard deviation of a portfolio with half of its funds invested in Security 1 and half in Security 3? (Leave no cells blank - be certain to enter "0" wherever required.)

e-1. What is the expected return of a portfolio with half of its funds invested in Security 2 and half in Security 3? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

e-2. What is the standard deviation of a portfolio with half of its funds invested in Security 2 and half in Security 3? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

There are three securities in the market. The following chart shows their possible payoffs:

a-1. What is the expected return of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

a-2. What is the standard deviation of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b-1. What are the covariances between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 5 decimal places, e.g., 32.16162.)

b-2. What are the correlations between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

c-1. What is the expected return of a portfolio with half of its funds invested in Security 1 and half in Security 2? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c-2. What is the standard deviation of a portfolio with half of its funds invested in Security 1 and half in Security 2? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

d-1. What is the expected return of a portfolio with half of its funds invested in Security 1 and half in Security 3? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

d-2. What is the standard deviation of a portfolio with half of its funds invested in Security 1 and half in Security 3? (Leave no cells blank - be certain to enter "0" wherever required.)

e-1. What is the expected return of a portfolio with half of its funds invested in Security 2 and half in Security 3? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

e-2. What is the standard deviation of a portfolio with half of its funds invested in Security 2 and half in Security 3? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Sensitivity is the probability that a test will identify a person who has the disease you are testing for.

Question 9 options:

Which of the following statements is NOT true when describing Specificity?

Question 10 options:

A) It measures the effectiveness of a test in returning a negative test result to people who do not have the disease.

B) It is the ability of a test to correctly identify people who have the disease you are testing for.

C) It is a characteristic of a diagnostic test, and is unaffected by the population you are testing.

D) It increases or decreases in relation to the sensitivity of your test.

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 650 babies were​ born, and 325 of them were girls. Use the sample data to construct a 99​% confidence interval estimate of the percentage of girls born. Based on the​ result, does the method appear to be​ effective?

pros and cons of risk probability and impact assessment, in Qualitative risk analysis?

The biggest disadvantage of a fixed exchange rate is the

Select one:

A. increased probability of high inflation.

B. tradeoff between supporting the exchange rate and adjusting the trade balance.

C. tradeoff between supporting the exchange rate and maintaining full employment.

D. increased probability of a trade deficit.

E. tradeoff between supporting the exchange rate and maintaining a balanced budget.

What is the probability that Sue gets a B grade of at least 4 out of 5 on a 5-question multiple choice test (with answers A - D for each question) by guessing at random? What is the sample space? What are the events that satisfy the condition of at least 4 out of 5 correct answers?