### Transformations - Joint and Marginal Probability Mass Function

Let X1 and X2 have the joint pmf p(x1,x2) = (x1x2)/36 x1=1,2,3 and x2=1,2,3, zero elsewhere. Find first the joint pmf of Y1=X1X2 and Y2=X2, and then find the marginal pmf of Y1.

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Let X1 and X2 have the joint pmf p(x1,x2) = (x1x2)/36 x1=1,2,3 and x2=1,2,3, zero elsewhere. Find first the joint pmf of Y1=X1X2 and Y2=X2, and then find the marginal pmf of Y1.

The National Collegiate association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard deviation of 8.2 hours. a. Using the sample

Question: Suppose we turn over cards simultaneously from two well shuffled decks of ordinary playing cards. We say we obtain an exact match on a particular turn if the same card appears from each deck: for example, the queen of spades against the queen of spades. Let pm equal the probability of at least one exact match. Show

CASE: Mrs. Jones, a robust 50 year old insurance adjuster living in the northern suburbs of Chicago has been diagnosed by a University cardiologist as having a defective heart valve. Although she is otherwise healthy, Jones's heart problem could prove fatal if left untreated. Firm research data are not yet available to predict

Cast a die a number of independent times until a six appears on the up side of the die. Find the probability density function F(x)= P(X<= x).

Let X have the pdf f(x)=2x if 0<x<1, zero elsewhere. Let Y=-2 ln X. Find the distribution function and pdf of Y.

a. A book of 450 pages contains 450 random misprint error(s). What is the probability of exactly 0 errors on a randomly selected page? b. What is the probability of at least 3 error(s) on any one page? c. What is the probability of between 1 and 4 (inclusive) random misprint error on any one page? Express you answer using 3 s

1.Go to this WHO website: http://www3.who.int/whosis/life/life_tables/life_tables.cfm?path=whosis,life,life_tables&language=english Look up the life table for Afghanistan. A.Plot the survival curve for males and for females. Briefly describe any differences or trends. B.What is the chance of surviving birth to age 60 f

I need you to explain to me step by step how to solve this problem. I am having trouble understanding this question. Question: A bag contains 40 blue marbles, 40 red marbles, and 20 green marbles. 60 of the marbles are big. These marbles are selected at random without replacement. What is the probability of randomly selecti

It's estimated that 57% of Americans live in households with 1 or 2 people, 32% live in households with 3 or 4 people and 11% live in households with 5 or more. Explain how you will find the expected number of people in an American household. The probability of winning when you bet on a single number in roulette is 1 in 3

Shaquille O'Neal is not recognized as good free throw shooter. Career average is 0.532 (53.2%). Suppose in a game Shaq takes 5 free throws. a. What type of probability distribution is this? Explain (Binomial???) b. What are the mean and standard deviation for the number of made free throws? c. What is the probability

1) One of the ways most Americans relieve stress is to reward themselves with sweets. According to one study, 46% admit to overeating sweet foods when stressed. Suppose that the 46% figure is correct and that a random sample of n = 100 Americans is selected. a) Does the distribution of p^, the sample proportion of Americans w

Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is ins

I am a mature student (age 60) currently working for a training company. I have been asked to complete a training project which involves these questions and have already done some of the work; however, I need to confirm my answers for these last few questions. I have attached the questions along with the SMOG and FOG data she

Give a probability distribution for the following: In 1992, the Big 10 collegiate sports conference moved to have women compose at least 40% of its athletes within 5 years. Suppose they exactly achieve the 40% figure, and that 5 athletes are picked at random from Big 10 universities. The number of women is recorded. For th

If a person adopts a pet there is a 45% it'll be a cat and 55% it will be a dog (a local dog and cat adoption). If a cat is adopted there is 60% chance it will be a female. If a dog is adopted there is 35% chance it is a female. A random selection is made and it was a male. What is the the probability that the selection is a

A) A fire station is to be located along a road of length A, A<∞. If fires will occur at points uniformly chosen of (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[|X-a|] when X is uniformly distributed over (0,A). b) N

If a particular batch of data is approximately normally distributed, we would find that approximately: a. 2 of every 3 observations would fall between ±1 standard deviation around the mean. b. 4 of every 5 observations would fall between ±1.28 standard deviations around the mean. c. 19 of every 20 observations would fall be

A professor grades homework by randomly choosing 5 out of 12 homework problems to grade. a) How many different groups of 5 are there from the 12 problems? b) Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? c) Silvia did 7 pro

Sample Problems - Please show all your work. QUESTION 1 Suppose that you are working for an energy company that distributes natural gas to residents in a city. As the chief economic analyst, you are asked to analyze the demand for natural gas in your city. Let X denote the random monthly demand for natural gas in millions of

1) Records show that 30% of all patients admitted to a medical clinic fail to pay their bills and that eventually the bills are forgiven. Suppose n = 4 new patients represent a random selection from the large set of prospective patients served by the clinic. Find these probabilities: a) All the patients' bills will eventually h

Show all your work 1) If x has a binomial distribution with p = .5, will the shape of the probability distribution be symmetric, skewed to the left, or skewed to the right? Explain why. 2) A meteorologist in Chicago recorded the number of days of rain during a 30 day period. If the random variable x is defined as the numbe

1) A shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment, but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24 hour period, what is the expected gain per

The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let's interpret this to mean that 95 percent of the flights are cleared in 45 minutes, so 5 percent of the flights take longer to clear. Let's also assume that the distribution is approximately normal. a) If the standard dev

A lifespan in hours for an electrical component is a random variable x, with cumulative dist. funct.: F(x) = {1-e^-x/100 for x>0 0 elsewhere Determine probability function x for x: Which of the Following Answers: a.) F(x) = {100e^-x/100 for x>0 0 elsewhere b.) F(x) = {1-1/100

I.) The number of construction projects on a college campus follows Poissan's dist. with a mean=3. The probability that exactly two projects are currently taking place is: 1.) 0.4230 2.) 0.224 3.) 0.00 4.) 0.1990 J.) In an assembly line with robots, a particular component can be installed in 90 seconds if holes a

F.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another.

D.) Suppose X1 and X2 are independent exp. random variables, each with mean data and y=X1 and X2. What is the moment generating function for the random variable y? Which choice below is right: 1.) My = (1-t/beta)^-2 2.) My = (1-t/beta)^2 3.) My = (1-beta*t)^-2 4.) My = (1-beta*t)^2 E.) Let X1 and X2 be two di

A fair coin is tossed 3 times. Let X be the number of heads on the third tossing and let Y be the total number of heads. Questions: a) Find the joint pdf of X and Y. b) Find the marginal pdf of X. Compute E(x) and V(x) - does X follow classical distribution? c) Find the marginal cdf of Y. Compute E(y) and V(y) - does Y

The density function of a continuous variable x is given by f(x) =x; 0≤x<1 and f(x) = 2-x; 1≤x<2 a) Find p(1/2≤x≤3/2) b) Find the median and quartiles of this distribution