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- Take the Gamblers ruin on [0, N] with a fair coin, i.e., a simple random walk with absorbing boundaries at 0 and N. Let T be the time which elapses before the SRW is absorbed by one of the boundaries (i.e., the duration of the game. Show that P(T < ∞) = 1 and Epecation (T^k) < ∞ for all k.The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3, L = 1.2 ± 0.1 cm, and A = 1.30 ± 0.05.a) Estimate M and find the uncertainty in the estimate.b) Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm³, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?An advert=isement cla=m that th=eir laptop co=mp=uter batteries are set at 72 operating hours, with proper charging procedures. A study of 5000 ba=tteries of th=ese laptop com=puters is carried out and 20 of them stop ope=ratin=g before 72 hours. Do these exp=erimen=tal results r=eject the c=laim that no more than 0.3 perce=t of the com=pany’s batt=eries will fail du=ring the adv=ertised time= period, with pr=oper char=ging proc=edure=s? hypo testing alpha 0.05 please write it onpaper
- 2. Give the condition which ensure that |ez| < 1 where z in C.An instructor has given a short quiz consisting of nvo parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points earned on the second part. Suppose that thejoint pmf of X and Yis given in the accompanying table. a. If the score recorded in the grade book is the total number of points earned on the nvo parts,what isthe expected recorded score E(X + Y)? b. If the maximum of the two scores is recorded,what isthe expected recorded score? A random variable is normally distributed with a mean of m =50 and a standard deviation of <T =5. Sketch a normal curve for the probability density Label the horizontal ax. is with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). What is the probability…The scenario relates to a waiting line at the Dipping star at Six Flags. For the purposes of the next two questions, assume that the Wicked Twister, which was permanently closed in September 2021, has since relocated and re-opened at a different venue in California. Suppose that a waiting line at the Dipping Star at Six Flags follows M/M/1 queue, with unlimited arrivals, and FIFO. Assume that on a busy holiday, visitors to the Dipping Star purchase tickets in person every five minutes on average. Also, assume that the employees at the ticket counters on average serve fifteen customers every hour. What is the expected average time a customer waits in line before it is their turn to purchase tickets? a. 2 minutes b. 3.3 minutes c. 8 minutes d. 16 minutes e. 26.6 minutes On average, how many customers are waiting in line? a. 1.5 b. 1.9 c. 3.2 d. 4.1 e. 3.25 students
- 36// Engineers working in a factory R&D unit are wanted, which is not noticed among their budgets. Accordingly, Mann Whitney U, which is significant in terms of difference between positions at 05 materiality level, is not for you. a) 24 B) 87 NS) 53 D) 76 TO) 16Determine S[y] has a local maximum or minimum on the stationary path. (by the value of the O(ϵ2) term in Δ)In what sense is the mean teh center of distributon? a.M is the center because half the sample scores are always above it and half are below b.M is center because it is always the most probable score in the sample c.M for the sample always equals micro for the population d.M is like a balance point because E (m-x)=0 for every sample.
