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When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size? = 25.
Consider a simple card game where there are four cards labeled 1, 2, 3, and 4. Each round, my friend first draws a card randomly from the four. After my friend draws the card, I also randomly draw a
The bank opens at 8am and you arrive at the bank at uniformly random time between 8am and 9am. Let X be the number of people who entered the bank before you. Find the expectation and the variance of
Find E(X) and Var(X). What is the probability of no defective product, the probability of at least one faulty product and find probability of at least three defective products. Calculate the probab
Let Xsub1 and Xsub2 be two continous random variables having the joint probability density
Use the distribution function techniques to find the probability density of the amount that the service station has left in its tanks at the end of the day
Consider two components whose lifetimes X and Y are independent and exponentially distributed with parameters lambda_x and lambda_y, respectively. Find the joint pdf of total lifetime X+Y and the p
An instructor stated at the beginning of a course that on the average 35% of students do not pass the exam. After the exam, a random sample of 100 students who took the exam was selected, and 25 of
If the above confidence interval is used to test the given hypotheses, what would the statistical decision be ? What would the level of significance of the hypothesis test be?
The Florida Fruit Supply Company uses bottles that are labeled as containing 23 oz of orange juice. A random sample of 24 such bottles shows that the sample mean and standard deviation are 22.75 oz
List the steps you would follow to determine the reliability of the exam. About 100 students will take this exam. The exam will take 90 minutes, which is the full length of the exam period. There
Hint: Show that Mzn(t)=exp(-sqr(n)*t - ln(1-t/sqr(n))) and then use the expansion ln(1-s)=-s-(1+E)s^2/2 where E->0 as s->0. Does the above limiting distribution also follow as a result of the
Show that Yn=e^(-Xnbar)converges stochastically to P[X=0]=e^-u. Find the assymptotic normal distribution of Yn.
Consider a stock with S_0 = 50 that pays a dividend of $1 at t = 1. Suppose the effective (not continuous) annual interest rate is r = 10% and the 3-year forward price is F(0,3) = 59. Construct an
You are looking for a home in a particular neighborhood, and you want to know the typical number of bathrooms and bedrooms, the square footage, and the appraised value of houses in that neighborhood
Calculating Percentiles A data set consists of the 85 ages of women at the time that they won an Oscar in the category of best actress.
Old Faithful Geyser; Time intervals (in minutes) between eruptions of Old Faithful geyser in Yellowstone National Park:
Find the standard normal curve area that lies
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 99 percent of the time? (Round your answer to the nearest whole number. Round z-value to 2 decimal place
What is the probability that you get in somewhere (at least one acceptance) What is the probability that you will be accepted by both Harvard and Duluth?
Suppose the National Basketball Association (NBA) reports that the average height of basketball players is 6'8". As a coach, you know that the players on your starting lineup have heights of 6'5", 6
If the maximum score on an exam is 100, what is the maximum mean score that you could possibly have after the next exam?
Old Faithful Geyser: Time intervals (in minutes) between eruptions of Old faithful geyser in Yellowstone National Park:
One student works as an executive secretary earning $75,000 per year. Which does a better job of describing the income of typical student in the class: the mean or the median? Why?
The random variable x has the following discrete probability distribution.