Solve the following independent system of equations. 5x−8y=−70 11x−4y=−18   Solution: x=   y=

Q: 9. Let X and Y have the joint density f (x, y) = cx(y=x)e (a) Find c. (b) Show that: fx|y (x | y) =…

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Q: A grocery clerk can serve 20 customers per hour on average and the service time follows an…

A: We have givenλ = 20/60 = 1/3 = 0.33 per minute X ~ Exponential (λ) Since we know that Cdf of…

Q: Problem 4 gA(Y) ~ Exp(1). Let Y Uniform(0,1). For 1>0, find a function ga: RR such that P

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Q: A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 44…

A: Degree of freedom,  df=n-1

Q: Assume that a sample is used t sample of size 103 with 70 suc decimals (not percents) accura 99%…

A: given data :CI=0.99α=1-0.99=0.01x= no. of success=70n=103p^=Xn  =70103 =0.6796

Q: Express the confidence interval 14.2 % < p < 32.2 % in the form of p + ME. %+ Submit Question 1%

A: The confidence interval for proportion in tri-linear  inequality as:  Lower bound &lt;p&lt; upper…

Q: An unknown distribution has a mean of 90 and a standard deviation of 15. A sample of size 80 is…

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Q: Dave's wardrobe contains 25 T-shirts, of which 12 are gray. Dave selects a T-shirt at random. What…

A: General formula of probability is ,   Probability = Number of favorable outcomes Total outcomes

Q: (a) Suppose that you choose three coins at random (without replacement) from a bag containing four…

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Q: Exercise 2: Show that .0965 is the joint probability density for two independent random variables X₁…

A: dnorm() is a R function that is used to calculate the probability density of a normally distributed…

Q: You run a factory that produces widgets (no, you'll never escape the widgets). Widget diameters are…

A: GivenMean(μ)=122standard deviation(σ)=10sample size(n)=16

Q: Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of…

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Q: Suppose A, B and C are sets. Prove that A (BC) = (AB) U (ANC). [Prove this using elements of these…

A: Given that, A, B, C are three sets.

Q: The average length of a hospital stay in the US is µ = 9 days with standard deviation of σ = 3 days.…

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Q: You wish to ask each of a large number of people a question to which the answer "yes" is…

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Q: A study found a positive correlation between IQ and making good economic choices. One possible…

A: Lurking variable can identify a strong relationship between variables or it can hide the true…

Q: table at a fair is testing out a new game that works as follows: the player rolls two six-sided…

A: Given for first roll probability of 6 = 1/6 and on second die it is also  1/6

Q: xample: A five-card poker hand dealt from a said to be a «full house» if it consists of thre Il the…

A: Given A five-card poker hand dealt from a deck of 52 playing cards The number of ways in which we…

Q: A normal distribution has a mea that a randomly selected value, 36. P(x≤85)

A: Given    Answer:- Given     X ~ N(μ, σ)                      Where mean μ   =75…

Q: The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Let X = the number of…

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Q: Is the probability for my standardized range really the same as for my original distribution? How…

A: introduction the above question is about probability  We have to explain is the probability for…

Q: A binomial experiment with probably of success p=0.36 and n=9 trial is conducted. What is the…

A: Givenp=0.36n=9x~Binomial(n=9,p=0.36)P(X=x)=(nx)×px×(1-p)n-x    ; x=0,1,...,n

Q: Find the critical value x corresponding to a sample size of 107 and a confidence level of 99%.…

A: Sample size n = 107 Degree of freedom df = n-1 = 107 - 1 = 106 99% confidence means P = 0.99…

Q: There are 2 sharpeners, 2 pencils,5 erasers and 4 notebooks. In how many ways a shopkeeper can…

A: Given Information: There are 2 sharpeners, 2 pencils,5 erasers and 4 notebooks. Required: To find…

Q: entral Limit Theorem with Propositions A researcher believes that 9% of males smoke cigarettes. If…

A: GIVEN DATA, A researcher believes that 9% of males smoke cigarettes.p=0.09n=664probability that the…

Q: A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the…

A: Possible samples of two odds are given below.

Q: Compute the expected value.

A: The given probability function can be described as X 1 2 3 f(x) 1/6 2/6 3/6

Q: Assume casinos keep 3.25% of the money wagered. The casino statewide kept 9.56 billion during the…

A: Answer: From the given data, Assume casinos keep 3.25% of the money wagered, The casino statewide…

Q: A coin has been weighted so that landing on "heads" is 4 times greater than landing on "tails".  You…

A: A coin has been weighted so that landing on "heads" is 4 times greater than landing on "tails". i.e.…

Q: Branching with immigration. Each generation of a branching process (with a single progenitor) is…

A: Note....  Same question is giving two times .   Giving  Answer  will be the same as they are not…

Q: Suppose that X₁, X2, X3 are independent and identically distributed random variables with…

A: Given Cdf  F(x)=1-2-x; x≥0

Q: Choose P, Q, and R uniformly at random within the convex region C illustrated beneath. By…

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Q: Twenty-five percent of the academic staff of a large faculty are non-teaching academic staff. A…

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Q: A researcher must estimate the mean temperature (in degrees Fahrenheit) with the following sample…

A: Data given 35.2,36.1,30.4,23.9,46,46.5,45,28.7,23.5

Q: From experience, the manager of Kramer's Book Mart knows that 60% of the people who are browsing in…

A: Given,n=10p=0.6q=1-0.6=0.4A random variable X~Binomial(n=10 , p=0.6)P(X=x)=Cx(0.6)x(0.4)10-x    ;…

Q: A die is tossed. Find the odds against rolling a number greater than 4. The odds against rolling a…

A: given data a die is tossed we have to find out the odds against  rolling a number greater than 4 =?

Q: The PDF of the two independent random variables X and Y are shown in the image below. fx(x) fy(y)…

A: From the given information, From the above plot, fx=12*12*1, -1≤x≤0,  since, area of right angle…

Q: After which time tB will the router fail for the second time with a probability of at least P =…

A: Let X be the time until failure is approximately well estimated with an exponential distribution…

Q: 1. Problem on equity forward: Calculate the no-arbitrage forward price for a 60-day forward on a…

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Q: A fair coin is tossed n times. Show that, under reasonable assumptions, the probability of exactly k…

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Q: 37. Let X₁,..., Xn be a random sample from the Laplace distribution (also called the double…

A: Given that X1, . . ., Xn be a random sample from the Laplace distribution with pdf fx; θ =e-x-θ…

Q: Suppose a, ne Z and 0 < a <n. Prove that n (2) = (^=¹1)+(21) a a-1 n- in two different ways: firstly…

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Q: The arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25…

A: Given that  The arrival rate of patients at a hospital counter follows Poisson distribution with a…

Q: A bag contains 6 white and 4 black balls.2 balls are drawn at random. Find the probability that they…

A: 10 balls=6(white)+4(black) nCr=n!/(r!(n-r)!) r!=r(r-1)×..3×2×1

Q: Give an example of a not mutually exclusive events probability. The topic should be related to…

A: Generally, a mountain consists of trees, animals ,waterfalls,etc. According to probability,two…

Q: If a farmer has a cylindrical silo that is 18ft  wide an 60ft tall. What is the maximun number of…

A: Given: A farmer has a cylindrical silo that is 18 ft  wide and 60 ft tall. Width of cylinder, w=18…

Q: A biased coin is tossed repeatedly. Each time there is a probability p of a head turning up. Let Pn…

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Q: The service time for a passport application in a certain government office is modelled as an…

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Q: Sickle cell anemia is an inherited disease in which red blood cells become distorted and deprived of…

A: Given dataSickle cell anemia is an inherited disease in which red blood cells become distorted and…

Q: If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are…

A: From the provided information, We are dealt 4 cards from a shuffled deck of 52 cards. Total queens =…