Prove that k (x)= - = n (n − 1) for integers n and k with 1 ≤ k ≤ n, using a: a) algebraic proof.

Q: The following data are the grades of the EDA students in Engr. A. Determine the Mean, Mode, Median…

A: Given data is96, 84, 85, 72, 95, 74, 75, 88, 87, 98, 81, 79, 78, 76, 81, 99, 74, 75, 82, 81, 95, 94,…

Q: 2. Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature…

A: Given,f(x,y)=1.5(x2+y2); 0≤x,y≤10; elsewhere

Q: A computer salesman averages 1.3 sales per week. Find the probability that in a randomly selected…

A: It is given that the A computer salesman averages 1.3 sales per week. So, if we denote the number of…

Q: Prove that k() = n(1) (n = 1) for integers n and k with 1 ≤ k ≤ n, using a: a) combinatorial proof;

A:

Q: the hypothesis test for an OLS parameter vn, and yet you know that the asymptotic Les are Normally…

A: The ordinary Least Square Method is the model for regression yn = β0+β1xn,1+...+βpxn,p+εn Standard…

Q: A bag of 25 tulips contains 11 red 8 yellow and 6 purple. If I select 2 bulbs what is the…

A: The number of red tulips is 11 and the number of yellow tulips is 8 and the number of purple tulips…

Q: A random sample of 105 automobile owners in a region shows that an automobile is driven on average…

A:

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: It looks like we lost. If you know someone else I can contact, please help.  The problem is burning…

A: Total numbers to be generated by machine =91,2,3,4,5,6,7,8,9 Probability of generating each number…

Q: When Susan and Jessica play a card game, Susan wins 60% of the time. If they play 9 games, what is…

A: Given: n=9p=0.6 w=pj=1-w=ppJassica wins exactly k games=Cn,k w^k 1-w^n-k Formula: SUMk=o to n Cn,k…

Q: 4) Given the following dataset of reported claim distribution, k is the number of claims, nk is the…

A: Regression model         A regression model is a function that describes the relationship between…

Q: Problem 4. A machine receives signals, and the number of signals it receives has a Poisson (.…

A: Given: The number of signals the machine receives has a Poisson distribution. The signal is either…

Q: Show that if X ∼ Geom (p) then P(X = n + k | X > n) = P(X=k)  for n, k≥1.

A: Given that  X ~ Geom (p)  By using the geometric distribution and it's recurrence relationship we…

Q: 4. In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year.…

A: Given that  A company paid overtime wages Or hired temporary helps=32 weeks Overtime paid wages=26…

Q: ose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and…

A: Here, μ=69 and σ=5. (a) The probability that an 18-year-old man selected at random is between 68 and…

Q: 1. A gaming company claimed that their role-playing games take over 65 hours to complete. A sample…

A: Null hypothesis H0:mu=65 Alternate hypothesis H1:mu>65 Calculating test statistics…

Q: ak surprising? Explain. Select the correct choice below and fill in the answer box(es) within your…

A: Given Maria plays basketball and is a 64% free throw shooter During a 25-game season, Maria had a…

Q: Find the moment generating function for the random variable X whose density function is f(x).  fx =…

A: Answer:

Q: If the marble we select is yellow, what is the probability that we chose the first bin?

A: here given , We have two bins. The first bin has 6 blue marbles and 4 yellow marbles. The second bin…

Q: a) the probability that the time to detect the next piece of debris is less than 3 minutes. b) the…

A:

Q: At a certain gas station, 65% of the customers use regular gas, and all the other customers use…

A:

Q: Use the given statement to represent a claim. Write its complement and state which is Ho and which…

A: From the provided information, The statement of the hypothesis is as follow: µ ≥ 203

Q: INSTRUCTION: Provide Descriptive Statistics using the Data Analysis in Excel for the “Systolic Blood…

A: Descriptive statistics are calculated below: Excel Procedure: Enter the data for systolic blood…

Q: A fair coin is tossed six times. Find the probability of getting four heads.

A:

Q: Let X₁, X₂ and X, be a random sample of size n=3 from a distribution with p.m.f. Construct a) b)…

A: Given that X1, X2 and X3 be a random sample of size n=3 from a distribution with p.m.f. PX=x=14  ;…

Q: In a seminar in engineering, the attendees are 15 civil engineers, 30 electronics engineers, and 20…

A: civil electronics electrical total Mapua university 5 12 7 24 Other…

Q: (i) Construct a 95% confidence interval of the difference in mean for the two solutions (ii) At the…

A: Calculate the Sample Mean and Sample Standard deviation for A and B Using Excel  i) Construct the…

Q: Let X be a continuous random variable with a density function { [/x-9/5, 0, (a) Find P(X> 10). (b)…

A: Given that  X is a continues random variable by using the cdf and expectation rule we solve this…

Q: In a certain city district, the need for money to buy drugs stated as the reason for 61% of all…

A: Given,n=5p=0.61q=1-0.61=0.39A random variable X~Binomial(n=5 , p=0.61)P(X=x)=Cx5 0.61x0.395-x  ;…

Q: Consider the given discrete probability distribution. Find the probability that x=5. 2 569 P(x) 0.05…

A:

Q: The following table contains the probability distribution for X = the number of re-transmissions…

A: As per our guidelines we are suppose to answer only one question1)Given data is x P(x) 0 0.40…

Q: random sample of size n = +Z₂+...+Z₂². Find P

A: Given: sample size n=7 To find P(1.69<W<14.07)

Q: A computer salesman averages 1.3 sales per week. Find the probability that in a randomly selected…

A: Given,The average no.of sales per week (λ)=1.3A random variable X~Poisson(λ=1.3)P(X=x)=e-1.31.3xx!…

Q: 20 :) Find the circumference of the circle pictured above. Round your answer to the nearest tenth

A: Given:The diameter of circle is given.d=20Here we find that circumference of the circle.

Q: A cordless telephone that is regularly priced at $50.00 is discounted $10.00. What is the discount…

A: Given  Telephone price=$50.00 Discount =$10.00

Q: In an election with three candidates, A, B, and C, the voters have the following preferences: 12%…

A: Votes received by candidate A = (12+19+17+25)% = 73% Votes received by candidate B = (17+19)% = 36%…

Q: College students were asked, "How often do you wear a seat belt when riding in a car driven by…

A: Given data: Response Frequency Never 106 Rarely 332 Sometimes 592 Most of the time 1215…

Q: Use a t-distribution and the given matched pair sample results to complete the test of the given…

A: Since you have posted a question with mutliple subparts, we will solve first three subparts for you.…

Q: Two discrete random variables X and Y have the joint probability density function: f(x.y)=e*p"…

A: Given: Two discrete random variables is X and Y   fx,y=λx e-λ py1-px-yy! x-y!…

Q: Suppose a drawer contains two brown socks, seven white socks, and three green socks. We draw one…

A: The provided information is  There are three drawer stocks 2 are brawn stocks 7 white sticks 3 green…

Q: probability problem person 1 is trying to loss weight, he needs to consume less than 2000 calories…

A: GivenTotal calories to be consumed for weight loss <2000  Total calories consumed daily =2500 The…

Q: A local university has 2,654 Hispanic students out of a total student population of 23,956. Do the…

A: Given: Total number of students in a local university is 23,956 Number of Hispanic students is 2,654…

Q: The shape of the distribution of the time required to get an oil change at a 20-minute oil-change…

A: Solutions Given The shape of the distribution of the time required to get an oil change at a…

Q: A random variable X has the probability density function given by: x) = {k(1-x) (k(1-x) if-1≤x≤1…

A: Given, f(x)=k(1-x)     -1≤x≤1 ∫-∞∞f(xi)=1

Q: A box contains a total of 100 CDs that were manufactured on two machines. Of them, 60 were…

A:

Q: Is it more, less, or equally likely that the sum after rolling 4 fair dice is 21 or that the sum…

A: To get a 21, the outcome must be a permutation of (6, 6, 6, 3) (4 possibilities), (6, 5, 5, 5) (4…

Q: Let X and S² be associated with a random sample of size n=16 from a distribution N(μ,0²). Find the…

A: According to the question, X̄ and S2 are associated with a random sample of size n = 16 drawn from…

Q: The sample space of a random experiment is the set of positive real numbers, S={x | x>0}. Define…

A: Given data Sample space S = {x|x>0} Event A ={x|x>40} Event B = {x|x<65}

Q: In 1936, the cost of a Hershey's chocolate bar was 5 cents. In 1980, the cost of a Hershey's…

A:

Q: Mildred rolls the dice 300 times. Approximately how many times it will be

A: Given information: Total no. of rolls=300favourable outcomes={3,4,5,6}