Two independent events ? D and ? E can only be disjoint if ℙ(?)= P ( D ) = AnswerAnswer ℙ(?)= P ( E ) = Answer

Q: At my local bar, it always takes at least two minutes to serve a customer, and it can take much…

A: Given information: ft=64t5, t≥2Ft=1-16t4, t≥2

Q: Two machines turn out all the products in a factory, with the first machine producing 35% of the…

A: event P(machine 1 ) = 0.35 P(machine 2 ) = 0.65 first machine produces 7% defective product second…

Q: 2. i. Show that p(x) = x=2 10 x3³ +1 62 ii. Show that f(x) = x = 3,4,5,6, is a valid probability…

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Q: A large insurance company maintains a central computing system that contains a variety of…

A: Given Information: Number of servers is k=3 Arrival rate for calls λ=33 Service rate for calls μ=22…

Q: Queen Dido, the founder of Carthage, was told that she could have as much land for Carthage as could…

A: a) Let L be the length of the rope in kilometers and A be the area encircled by the rope along the…

Q: An employment company has six men and 5 women who want to be assigned to a certain task. One…

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Q: A certain transmission system has 2 transmission modes. In Mode 1, the transmitted signal X is…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X₁, X₂, X3,..., Xn denote a random sample of size n from the population distributed with the…

A: It is given that the probability density function of X is f(x; θ) = { (θ + 1)•xθ,  if 0 < x <…

Q: A pair of dice is rolled. What is the probability of getting a sum of 12? What is the probability of…

A: From the provided information, A pair of dice is rolled. Total outcomes = 6 × 6 = 36

Q: The accompanying tree diagram represents a two-stage experiment. (Let x = 0.3, y = 0.7, r = 0.7, s =…

A: Given x = 0.3,  y = 0.7,  r = 0.7,  s = 0.3,  t = 0.4, w = 0.6

Q: C1. A collector wants to collect football stickers to fill an album. There are n unique stickers to…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: i) Show that the standard score of the sample mean X, is equal to Y.

A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1,

Q: 5A spinner is divided into five equal sectors labeled 1 to 5. What is the probability of spinning…

A: Given : Spinner has 5 equal parts with numbers 1-5   Note :As per guidelines only first question(5A)…

Q: a) Suppose that Y₁, Y₂, ..., Yn is a random sample from a normal distribution with parameter mean 0…

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Q: 10. Given the normally distributed random variable X with mean 20 and standard deviation 2.5, find…

A: given data, normal distribution μ=20σ=2.5we have to find out the value of k for the given data

Q: You are dealt one card from a 52-card deck. Find the probability that you are not dealt a ten.

A: You are dealt one card from a 52-card deck.  the probability that you are not dealt a 10.

Q: The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a…

A: Solution-: Given that: μ=55,σ=9 We want to find what is the approximate percentage of 1-mile long…

Q: A large portfolio of policies is such that a proportion of p, 0<p<1 incurred claims during the last…

A: Solution: Let X be the number of policies with claim. From the given information, n=25 and p=0.1.

Q: Problem 3 i.e. Let W, be a negative-binomial variable with parameter p € (0,1), -{C-1) P²α-p P{W, =…

A: We have Wr negative binomial random variable with parameter r and p and PMF given by…

Q: 5.) How many different 4-letter radio station call letters are possible if: (a) The first letter…

A: It is given that  4-letter radio station call letters.

Q: Salaries for teachers in a particular elementary school district are normally distributed with a…

A: given data  normal distribution μ = 44000σ = 6500n = 10 find 90th percentile for individual teachers…

Q: size, that is picking up a book is a random choice. (a) If you randomly pick up 5 books, what is the…

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Q: The length, in feet, of a certain structural steel beam is normally distributed with a mean of 10…

A: Given Mean=10 Standard deviations=5

Q: The table below shows the number of credit cards owned by a group of individuals. If one person was…

A: Given data is   Zero one Two+ Total Male 9 5 19 33 Female 18 10 20 48 Total 27 15 39 81

Q: i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and…

A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1, And the moment genarating function…

Q: (1)) This problem concerns a standard deck of 52 cards. A hand consists of 5 cards. When you…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: B Find the probabilities in Problems 17-22 by referring to the fol- lowing tree diagram and using…

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Q: Suppose that 11% of a certain batch of calculators have a defective case, and that 12% have…

A: P(Case defective)=11%, P(Battery defective)=12%  P(both defective)=5%

Q: 1. Which of the following functions are cumulative distribution functions? (Hint: Sketch the graph…

A: Given the functions : (a)        FXx=2x5,  x&lt;212,   2≤x&lt;31,     x≥3 (b)       FYy=0,…

Q: IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual…

A: As per our guidelines we are suppose to answer only three sub parts. Given,Mean(μ)=100Standard…

Q: Uniform Distribution. If the random variable x is uniformly distributed for values greater than 20…

A: Given:   continuous Random variable X from uniform (20, 80) Cdf of x : F(x)= (x-20)/(80-20)…

Q: Of the 25 computers available in the supply room, 10 have circuit boards for a printer, 5 have…

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Q: A very large charity has pledges (in dollars) with a mean of 89 and a standard deviation of 23.…

A: Given information: Mean = 89, S.D = 23 n = 121

Q: Among all the computer chips produced by a certain factory, 6 percent are defective. A sample of 400…

A: From the information, n=400 and p=0.06.

Q: 25 (1) ²5, respectively. i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X4 +…

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Q: 2. Caroline and Sarah have agreed to meet between 5:30pm and 6:30pm for dinner at Witherspoon…

A: Given that the random variables X and Y represents Caroline's and Sarah's arrival time relative to…

Q: iii) What is the value of the sample size m, if P(|Ỹ — µỹ| ≥ 10) < 0.04?

A: First we have to calculate the mean and variance of Y then we will use the Chebychev's inequality to…

Q: If X1,X2,...,Xn constitute a random sample of size n from a gamma population with α =2, use the…

A: Xi ~ gamma(ɑ=2 , β) ; i=1,2,...,n

Q: Use the attached random digit table to estimate the probability of the event that at least 2 people…

A: Random digit table is read from left to right and from top to bottom.

Q: 55 use microwave ovens; 66 use electric ranges; 56 use gas ranges; 18 use microwave ovens and…

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Q: Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume…

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

Q: How do I convert these to fractions?

A: The answers are already provided in the form of fractions.

Q: special deck of 20 cards has 5 that are red, 5 yellow, 5 green, and 5 blue. The five cards of each…

A: It is given that a special deck of 20 cards has 5 that are red, 5 yellow, 5 green, and 5 blue.Red…

Q: A six-sided die is rolled twice. What is the probability of showing a 6 on both rolls?   2.A fair…

A: If 6 sided die is rolled twice then the possible outcomes…

Q: Show that In (X;) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential…

A: It is given that X has the pdf  f(x) = (θ + 1).xθ , 0 &lt; x &lt; 1

Q: 1.2.1. Find the union C₁ UC2 and the intersection C₁ C₂ of the two sets C₁ and C2, where (a) C₁ =…

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Q: The digits 3, 4, 5, 6, 7, 8, and 9 are randomly arranged to form a three-digit number. (Digits are…

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Q: 2. Prove by induction that 3² i=0 3n+1-1 2 for all n with n ≥ 0.

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Q: The probability density function of a continuous random variable X is given by y=4−2x    from x=1…

A: A continuous function f(x) is the probability density function of the continuous random variable X…

Q: We have the weights of 18 individuals (9 men and 9 women) weight women: 38.9, 61.2, 73.3, 21.8,…

A: