Please see the attached file for probability questions. 1. Consider the probability density function for the uniform distribution on the range (a,b), b > a, fx (x) = (b - a)^-1, a < x < b. a) Sketch the probability density function fx (x). b) Derive the mean of the distribution in terms of a and b. c) Given a random s
Suppose an individual investor starts with a portfolio that consists of one randomly selected stock. a. What will happen to the portfolio's risk if more and more randomly selected stocks are added? b. What are the implications for investors? Do portfolio effects have an impact on the way investors should think about the risk
According to Bob, the payoffs of the several outcomes are as follows: a. If it is sunny and he is not carrying and umbrella, 10 b. If it is sunny and he is carrying an umbrella, 8 c. If it is rainy and he is not carrying an umbrella, 2 d. If it is rainy and he is carrying an umbrella, 6 Draw the game matrix of t
1. The random variable X has mean u and variance sigma^2. The random variable Y is defined as Y=g(x). (a) Use a first order Taylor Series expansion about u to prove the following (see attachment). (b) If X follows the exponential distribution with mean u, so sigma^2 = u^2, and Y = g(x) = sqrt(x), use the results in the qu
I've struggled for 3 days to come up with something approaching a relevant answer but am now desperate. Could you solve Q3, both a) and b) parts from the Exercise Sheet attached? Happy to pay 2 credits for both answers. Thank you very much. 3. The random variable X has an exponential distribution with mean µ. Let Y
In a recent survey, 80% of the community favoured building a new health centre in their neighbourhood. If 15 citizens are chosen, what are the mean and standard deviation of the number favouring the health centre?
According to government data, the probability that an adult has never been in a museum is 15%. In a random survey of 10 adults, what is the probability that at least 8 visited a museum?
Please help with the following: A polling company split a random sample in half and asked 477 respondents the question generally speaking, do you believe the death is applied fairly or unfairly in this country today? The pollesters asked the other 477 respondents the question, generally speaking do you believe the death penal
Please help with the following: 1. Of 515 Broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause food borne illnesses 85% were infected with a particular bacterium. A) Construct a 90% confidence interval? The 90% confidence interval is from _
1. The weight of potato chips in a small size bag is stated to be 5 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 5.1 ounces and a standard deviation of 0.08 ounces. a) What fraction of all bags sold are underweight? b) Some of the chips are sold in "bargain
The score distribution shown in the table is for all students who took a yearly AP stats exam. Score Percent of Students 5 13.3 2 21.9 3 24.9 2 17.8 1 22.1 Find the mean AND standard deviation:
The score distribution shown in the table is for all students who took a yearly AP stats exam. Score Percent of Students 5 12.4 2 21.7 3 25.4 2 18.4 1 22.1 Find the mean AND standard deviation:
Two persons, A and B, agree to meet at a place between 10 a.m to 11 a.m. The first one to arrive waits for 20 minutes and then leave. If the time of their arrival is independent and at random, what is the probability that A and B meet?
1. You roll a die, winning nothing if the number of spots is odd, $3 for a 2 or a 4 and a $18 for a 6. a) Find the expected value and standard deviation of your prospective winnings b) You play three times. Find the mean and standard deviation of your total winnings. c) You play 60 times. What is the probability that you wi
Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a s
How would you explain the analysis of variance, assuming that your audience has not had a statistics class before?
1) A company that sells different types of slippers wants to see how their new line of comfortable walking slippers sells so the company keeps changing the price on this certain product several times to find the best price for it. The company records the quantity it sells for each price level and then performs a linear reg
1) Adult American males have normally distributed heights with a mean of 5.8 feet and a standard deviation of 0.2 feet. What is the probability that a randomly chosen adult American male will have a height between 5.6 feet and 6.0 feet? A. 0.6826 B. 0.5000 C. 0.9544 D. 0.7500 2) A jar contains 12 red jelly beans, 20 yell
An experiment was carried out to assess the impact of the variables x1 = force(gm), X2 = power (mW), x3 = temperature (C) and x4 = time (msec) on y = ball bond shear strength (gm). The results are given in the problem 5 Excel data file. a. Perform a complete analysis. b. Perform a complete residual analysis. c. Check for col
The dataset contained in the problem #4 Excel file gives data on moisture content for specimens of a certain type of fabric. a. Create an X-bar R chart, using the first 10 subgroups as the base period. Comment on what is shown. b. What did you assume to construct these control limits (be specific)? Check the assumptions.
1. An experiment was designed to see what factors affect the cleaning ability of a washing solution. Three factors were used in the experiment - the concentration of detergent, concentration of sodium carbonate, and concentration of sodium carboxymethyl cellulose. A larger value of the response indicates better cleaning abilit
Player B Player A Strategy b1 Strategy b2 Strategy b3 Strategy a1 1 3 ï€ï€¶ -6 Strategy a2 2 -1 2 Strategy a3 2 7 ï€ -5 1. Is there an optimal pure strategy for this game? 2. If so, what is it? 3. Identify and eliminate dominated strategies an
In our virtual world, we own a construction company and bid on projects. Based on our past history of winning bids on projects, the probability of winning the next contract to build a school is 0.40, to build a hospital is 0.30 and to build both a school and a hospital is 0.20. What is the probability of winning a contract to bu
Describe the historical development of statistics and probability In non-Western cultures
1) A coworker is considering the use of a log linear (power) model using weight to estimate the cost of a missile engine. They have performed the following calculations in log space using natural logarithms. Select the corresponding unit space form of this power model equation. Log Space b1 = 1.109438 b0 = -0.122932 Cost
Two cards are drawn from single deck of 52 cards one after the other. - Find the probability of selecting a king from the first card. - If the first card is king and the card is not replaced, what is the probability of selecting a king from the second card? - Find the probability of selecting a king from the first card
Independent Events (I) or Dependent Events (D) 1) A spinner is flicked three times, and each outcome is recorded. _____ 2) One thousand numbered raffle tickets are sold. Three different items are raffled off by randomly selecting three different raffle tickets. _____ 3) A paper bag holds 4 slips of paper that are numb
Consider the following data from 50 Bernoulli Trials Let theta be the probability of the observing a one for any single trial. a) Find the likelihood of any sequence of s trials containing y ones. b) If the prior on theta is uniform such that p(theta)=1, find an expression for the posterior distribution for theta after 10 t
A statistical process analyst is responsible for assuring statistical control. In one process, a machine is supposed to drop 11.4 ounces of mints into a bag. (Assume that this process can be approximated by a normal distribution). The acceptable ranges for weights of the bags of mints are 11.25 ounces to 11.55 ounces, inclusive.
Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check