Use the mixed congruential method to generate a sequence of 32 random numbers with Xo=8, a=9, c=13, and m=32,. Check: a) If the Hull-Dobell Theorem holds b) the null hypothesis test calculating D+, D-, D and the value in tables with a level of significance of 5%.
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- Use the mixed congruential method with seed 26 constant multiply 17 increment 45 and modulus100. To generate 10 uniformly distributed random variables on (0,1).b) Use the linear congruential method to generate a sequence of 5 random numbers with given seed of 27, increment 43 and constant multiplier 17, modulus 100c) i. If an M/M/1 queue has utilization of 90%, what do you think will be the average queue length and the average response time? If the arrival rate is 100 jobs per secondii. If an M/D/1 queue has utilization of 80% do you expect its mean queue length and response time to be less, same, or greater than that of an M/M/1? Explain your answer.Generate the first five random numbers (0 to 1) using Linear Congruential method. Given: a = 7, c = 6, m = 17, X0 = 110
- A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d belowUse the LCM to generate 40-non-repeated random numbers with any value of xo, a, c, and m (m must be greater than 400 and m mod 100 # 0). Test for uniformity at a = 0.05 and independence at a = 0.10.In a cement factory, from a randomly selected 275 people, at least 150 of them have at least 1 kid. Test the hypothesis at %95 confidience that 50 percent of the workers have at least 1 kid. (Use the Ztable please)
- An industry representative claims that 34 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners. (a) Suppose that the representative's claim is true, and suppose that a sample of 4 dish owners is randomly selected. Assuming independence, use an appropriate formula to compute.In a toy shop ,2% of the toys are defective.If a boy selects 4 toys randomly ,find the probabiility of getting atleast one of the toys defective .In the Program Evaluation and Review Technique (PERT), we are interestedin the total time to complete a project that is comprised of a large number ofsubprojects. For illustration, let X1, X2, X3 be three independent random times forthree subprojects. If these subprojects are in series (the first one must be completedbefore the second starts, etc.), then we are interested in the sum Y = X1+X2+X3.If these are in parallel (can be worked on simultaneously), then we are interested inZ = max(X1, X2, X3). In the case each of these random variables has the uniformdistribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere, find (a) the pdf of Yand (b) the pdf of Z.
- A research center claims that 26% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 28% say that they would travel into space on a commercial flight if they could afford it. At α=0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below.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…Let X1, X2, ..., Xn be independent and identically distributed random variables, X ∼ Exp(λ). Show that the sum X1 + X2 + · · · + Xn is Γ(n, λ) distributed.