………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… (8 marks) (c) The nucleus is labelled on the diagram. Complete the table by putting a tick () or a cross () in each box to identify which properties belong to eukaryotic and prokaryotic cells. Structure or function Nucleolus Nuclear envelope Nucleoid Presence of DNA (4 marks) Eukaryotic cells Prokaryotic cells
www.asbiology101.wordpress.com
(d) The nucleus from the image is reproduced below. It has been magnified x 20,000
x 20,000
X
Y
Use the line XY as the length of the nucleus to work out its actual size. Show your working.
...the joint distribution for X and Y .
4.12 If a dealer’s proﬁt, in units of $5000, on a new automobile can be looked upon as a random variable
X having the density function
fx= 21x,0<x<10,elsewhere
ﬁnd the average proﬁt per automobile.
4.14 Find the proportion X of individuals who can be expected to respond to a certain mailorder solicitation if X has the density function.
fx= 2(x+2)50<x<10,elsewhere
4.28 Consider the information in Exercise 3.28 on page 93. The problem deals with the weight in ounces
of the product in a cereal box, with
fx= 25,23.75 ≤x ≤26.250,elsewhere.
4.33 Use Deﬁnition 4.3 on page 120 to ﬁnd the variance of the random variable X of Exercise 4.7 on page
117.
4.7 By investing in a particular stock, a person can make a proﬁt in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain?
4.37 A dealer’s proﬁt, in units of $5000, on a new automobile is a random variable X having the density
function given in Exercise 4.12 on page 117. Find the variance of X.
4.12 If a dealer’s proﬁt, in units of $5000, on a new automobile can be looked upon as a random variable
X having the density function
fx= 21x,0<x<10,elsewhere
ﬁnd the average proﬁt per automobile.
4.38 The proportion of people who respond to a certain mailorder solicitation is a random variable X having the density function given in...
...Course Name: Quantitative investment analysis FIN617 Winter 2013
Professor: Robert Elliott
Subject: final essay
Name: Feifei Chen
The essential of a random walk is the changes of stocks are irregular following Brownian movement; the path of price changes is unpredictable. Mentioning prediction of the future, an autoregressive timeseries is a significant and effective model. For a random walk without drift, however, standard regression analysis on the timeseries is unavailable, because it’s against the assumption of time series model, covariance stationary. Because the variance of the time series is lack of upper bound, which violates the principle that the variance of a covariance stationary series must be a constant. Meanwhile a random walk doesn’t have a finite meanreverting level. So we cannot use the AR model to predict the future for a random walk. Because based on AR(1) model, for a random walk without drift, the best prediction of future value is current value and this result doesn’t have any economic meaning. So it can be concluded that for a random walk, the changes of future should be unpredictable. As the change of stock prices follows a random walk, the change of stock price is undoubtedly unpredictable.
Considering from another perspective, if the stock prices follow a random walk, it is impossible for investors to predict the future...
...
Event A is rolling a die and getting a 6. Suggest another event (Event B) that would be independent from Event A.
A company runs 3 servers, each providing services to 40 computers. For each server, two of its client computers are infected. What is the probability that 3 randomly chosen client computers serviced by different servers (one per server) will all be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A.
What is the probability of getting 6 tails in 10 trials of tossing a coin? Solve this problem by using :The approximation mentioned in Theorem 6
The Binomial Distribution
Then compare answers for a) and b) after you have solved the problem.
When transmitting messages from a point A to a point B, out of every 40 messages 6 need to be corrected by applying error correcting codes. What is the probability that in a batch of 200 messages sent from A to B, there will be between 38 and 42 messages that will have to be corrected? Please choose the appropriate method to approximate this quantity.
The probability of an event occurring in each of a series of independent trials is . Find the distribution function of the number of occurrences of in 9 trials. That is, provide a...
...–drink vending machine is set so that the amount of drink dispensed is a random variable with a mean of 200 milliliters and a standard deviation of 15 milliliters. What is the probability that the mean amount dispensed in a random sample of size 36 is at least 204 milliliters?
[0.0548]
4. An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean (μ) = 117 cm and standard deviation (σ) = 6.1 cm. Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120 cm.
[0.16354]
5. The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3. What is the probability that in a random sample of 25 students, more than 275 pizzas are consumed?
[0.04746]
6. The number of customers who enter a supermarket each hour is normally distributed with a mean of 600 and a standard deviation of 200. The supermarket is open 16 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10000? [0.30854]
Contd . . . 2
 2 
7. The manufacturer of cans that are supposed to have a net weight of 6 ounces claims that the net weight is actually a normal random variable...
...Lecture Illustration – Random Digits Table
Simple Random Sampling can be conducted by two methods:
i) Drawing from Hats
ii) Random Digits Table
Refer to your Random Digits Table in Appendix.
Illustration 1
Suppose we have a population of 30 students from Curtin University Foundation Program:
Allen Connie Diaz Howard Law Piper 
Andres Cowel Dunst Jolie Miller Pitt 
Brandon Craig Evans Kay Moyles Ross 
Brooks Cyril Hanks Kathy Murray Smith 
Cole Depp Hilton Lavigne Nash Spears 
We would like to select a sample of 5 students using Simple Random Sampling:
Using the 1st Method: Drawing from Hats –
Simply put all the students’ name into a hat, shuffle the hat properly and draw out 5 names on a random basis.
Using the 2nd Method: Random Digits Table: 
1st Step: Label the population with numbers from 01 to 30.
2nd Step: Determine the number of digits to be used.
Since the population is 30....
...APStatistics Cole Rogers
Unit 7 Exam Random Variables: Free Response
Directions: Complete the assignment on this paper. If you need additional paper make sure that you clearly label each page with your name. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit.
1. A Roulette wheel has 38 slots numbered 0 to 36 and 00. The wheel is spun and a ball is thrown into the wheel and comes to rest in one of the slots. There are numerous of ways to bet, individual numbers, groups of numbers (112, 1324, etc), by color (half of the numbers are black and the half are red), and in various other combinations. This problem is going to focus on betting $1.00 on the number group 112. If the ball lands in any of the values 112 the bet is won and the return is $3.00. If the ball lands on any of the other values the bet is lost.
a.) Compute the expected value of this game. (4 points)
X
2
1
P(x)
12/38
26/38
X*P(x)
.631
.684
.053
The expected value is .053.
b.) Interpret this expected value. (4 points)
This means that the casino wins 5.3 cents per game or the players lose 5.3 cents per game.
c.) What is the average return to the casino from 1,000,000 such bets? (4 points)
1000000*.05=50000
The casino can expect to win 500000 of the 1 million bets because 1 million times .05 is 50,000.
2. A venture capital fund has the mandate to invest...
...The number of possible combinations of 3 horses winning, in any order, is
So the probability is
4. In how many distinguishable ways can the letters in the word statistics be written?
5. The table shows the results of a survey that asked 2850 people whether they are involved in any type of charity work.
 Frequently  Occasionally  Not at all  Total 
Male  221  456  795  1472 
Female  207  430  741  1378 
Total  428  886  1536  2850 
A person is selected at random from the sample.
a) What is the probability the person is female or occasionally involved in charity work?
b) Are the events “being female and occasionally involved in charity work” and “being frequently involved in charity work” mutually exclusive?
yes
6. A company gave psychological tests to perspective employees. The random variable x represents the possible test scores.
a) Use the histogram to find the probability that a person selected at random from the survey’s sample had a test score of more than two.
b) Find the probability that the person had a test score of at most 2.
7. The following table is a frequency distribution for the number of dogs per household in a small town.
Dogs  0  1  2 
Households  931  297  180 
a) Construct the probability distribution. (round to the thousandths place)
x  0  1  2 
P(x)  931/1408=0.661  297/1408=0.211  180/1408=0.128...
...Random Walks in Stock Market Prices
FOR MANY YEARS economists, statisticians, and teach
ers of finance have been interested in developing and testing models of stock price behavior. One
important model that has evolved from this research is the theory of random walks. This theory casts serious doubt on many other methods for describing and predicting stock price behavior
methods that have considerable popularity outside the academic world. For example, we shall see later that if the random walk theory is an accurate description of reality, then the various "technical" or "chartist" procedures for pre dicting stock prices are completely without value.

In general the theory of random walks raises chal lenging questions for anyone who has more than a
passing interest in understanding the behavior of stock prices. Unfortunately, however, most discussions of the theory have appeared in technical academic journals and in a form which the nonmathematician would usually find incomprehensible. This article describes, briefly and simply, the theory of random walks and some of the important issues it raises concerning the work of market analysts. To preserve brevity some aspects of the theory and its implications are omitted. More complete (and also more technical) discussions of the theory of random walks are available elsewhere; hopefully the introduction provided here will...