### Density Function : Median and Quartiles

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

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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

A manufacturer of computer printers claims that only 0.55% of all printers they produce fail out of the factory. As a computer store buyer, you purchase 150 of this company's printers. What is the chance that you get at least one defective printer out of this purchase? P(X is greater than or equal to 1)=____________ pleas

A jar contains marbles of different colors: 4 white, 6 black, 6 red, and 4 blue. On two random drawings, without replacement, find the probability that the first is black and the second is white. Assume that the draws are independent.

Take a deck of cards. A deeck has 52 cards with two major colors(Red and Black), with 26 cards each. Red colors comes in two shapes(heart and diamond), while black color shapes are called clubs and spades. Find the probability of obtaining Red or Queen. That is, find Probability(Red or Queen).

Two dice are rolled. Observe their output space and do the following: a) Probability ( sum of numbers making at most 8) b) Probability ( sum of numbers exceeds 8) c) Probability ( both dice having equal odd numbers) d) Probability ( even numbers on both)

The animal colony in the reseach department contains 20 male rats and 30 female rats. Of the 20 males, 15 are white and 5 spotted. Of the 30 females, 15 are white, and 15 are spotted. Suppose that you randomly select 1 rate from this colony: a)Find the Joint probability table including the marginal probability. b) what is th

The weight of the food packed in certain containers is a normally distributed random variable with a mean weight of 400 pounds and the standard deviation of 4 pounds. Suppose that the container is picked at random. Find the probability that it contains: a) more than 410 pounds b) less than 398 pounds c) between 391 and 398

How many ways can 6 distinguishable balls be placed in 5 boxes such that there are 2 balls in the first box, and one in all remaining boxes?

Many people believe that the daily charge of a price of a company's stock on the stock market is a random variable with mean 0 and variance {see attachment}. That is, if Yn represents the price of the stock on the n-th day, then (see equation in attachment( where X1,X2,..., are independent and identically distributed random var

Suppose the lifetime income of all high school grads is normally distributed and that the lifetime income of all college grads is normally distributed. Suppose that the difference in the means is known to be $600,000 and that the standard deviation of the high school graduates is $300,000 and the standard deviation of the colle

The Skateworld Company operates ice rinks in several major cities throughout the United States. During each session of open skating, one customer is selected at random to receive a free pass for a future open skating session. At a recent session there were 150 males and 130 females skating. What is the probability that the pe

Let X1,X2... be a sequence of independent and identically distributed continuous random variables. Define the random variable ... (a) Compute the p.m.f of N by first computing P(N [less than or equal to] n) (b) Show that E(N)=e *(Please see attachement for complete problem)

Find the conditional distribution of Y given X = ... (Joint density of X and Y given) *(Please see attachment for complete problem)

1. Choose a number at random from the set of numbers from the set of numbers {1,2,3,4,5}. Now choose a number from the subset {1,...,X). Call this second number Y. a) Find the joint p.m.f. of X and Y b) Find the conditional mass function of X given that Y = i. Do it for i = 1,2,3,4,5 c) Are X and Y independent? Why?

Subject: Probability Details: You appear on a game show and for your prize the host lets you choose one of three doors. Behind one door is a new car; behind each of the other doors is a goat. You choose a door. The host, who knows what's behind each door, then opens another door, which has a goat. He then asks if you want to p

I)Let X be an exponential random variable with mean 1,and Y = exp^(X/2): a)find F(y) b)Evaluate E(Y) c)Evaluate E[(Y^2)/(1+(X^2))] II)The random variable X is uniformly distributed on the interval [1,3].Find the probability density function fy(y)of the random variable Y=2X+5

According to hypothetical information, 18% of all Americans have hazel colored eyes. A SRS of 25,000 Americans are surveyed and asked about their eye color (assume each of the Americans in the sample has an 18% chance of having hazel colored eyes). a) Determine the mean and standard deviation of this sample of Americans that

The scores of students taking the Scholastic Aptitude Test (SAT) are normally distributed with a mean u = 1035 and a standard deviation o = 131. a) Determine the probability that a simple random sample of 15 students would earn an average score of 1000 or less. b) Determine the probability that a simple random sample

Suppose you pay $10 to play a card game with the following rules: You draw 2 cards out of a standard deck of 52 cards without replacement. If the 2 cards are of the same suit (i.e. both clubs, both diamonds, etc) you win $15 (a $5 profit). If the 2 cards are the same value (i.e. both jacks, both 2's, etc) you win $18 (a

This is for question #3 on the attached page... You will need the following fact for Question #3. integral_{-infinity}^{+infinity} e^(-x^2/2 sigma^2) dx / sqrt(2*pi*sigma^2) = 1 This is in Section 5.4: it just says that the function e^(-x^2/2 sigma^2) / sqrt(2*pi*sigma^2) is a density (it is the "famous" normal de

The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by f(x) = (ax2e−bx2 x>_0 { 0 x < 0 where b = m/2kT and k, T and m denote, respectively, Boltzmann's constant, the absolute temperature, and the mass of the molecule. Evaluate a i

A cdf Fx is stochastically greater than a cdf Fy if (1) Fx(t)<= Fy(t) for all t, and (2) there exists some t for which Fx(t) < Fy(t) (a)show that if Fx is the cdf of X and Fy is the cdf of Y, then (1) P(X>t) >= P(Y>t) for all t and (2) P(X>t) > P(Y>t) for some t.(in other words, X tend to be bigger than Y) Give an example.

How to calculate mean and variance of geometric distribution (by differentiating moment-generating function)?

From 5 statisticians and 6 economists, a committee consisting of 3 statisticians and 2 economists is to be formed. How many different committees can be formed if: (a) there are no restrictions (b) 2 particular statisticians must be on the committee (c) 1 particular economist cannot be on the committee Answers: (a) 150 (

2. Mistakes made by data entry clerks follows a Poisson distribution with a mean 0.8 per hour. You just gave someone applying for your data entry vacancy an hours worth of data entry material. Answer the following questions. A) What is the probability they will not make any mistakes? B) What is the probability they will

The prizes that can be won in a sweepstakes are listed below with the chances of winning each one: $4000 (1 chance in 8200); $1700 (1 in 5300); $800 (1 in 4100); $200 (1 in 2200). Find expected value of the amount won for one entry if the cost to enter is 55 cents. Answer is 0.54. Please explain the procedure (without only showi

You are reviewing a scientific study where the epidemiologists sampled 1000 people from Charleston, South Carolina and measured variation at two loci, A and B. The haplotype frequencies in the sample population are: AB = 0.406 Ab = 0.214 aB = 0.214 ab = 0.166 Toward the end of the article you are reviewing, you read th

It has been determined empiracally that for a certain egg producer, the number of cracked or broken eggs X, in a randomly slected box containing six eggs, follows approximately the distribution given in the table below: X: 0 1 2 3 4 5 6 P(X): 0.9 0.07 0.02 0.005 0.003 0.001 0.001

See attachment for Case detail: DataStor Company Case Questions 1. Assuming that the DS4000 manufacturing process is functioning properly, what is the probability that DataStor falsely detects an early warning signal to a problem with quality using the tracking system that Escalera described? (Hint: DataStor will 'falsely d

The manufacturer of the ColorSmart-5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consumers, 316 say that thei