22. A number is to be selected from the interval {x: 0 < x < 2} by a random process.Let A = {x: (i-1)/2 < x≤ i/2}, i = 1,2,3, and let A4 = {x: < x < 2}.For i = 1, 2, 3, 4, suppose a certain hypothesis assigns probabilities pio to these setsin accordance with Pio SA, 2dx, i = 1, 2, 3, 4. This hypothesis (concerning themultinomial pdf with k = 4) is to be tested at the 5% level of significance by a chi-square test. If the observed frequencies of the sets Ai, i = 1, 2, 3, 4, are respectively30, 30, 10, 10, would Ho be accepted at the (approximate) 5% level of significance?=

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(3.) A system contains components connected in parallel as shown in the diagram. If all components operate inderentently, & each component has probability 0.45 of failing What is the minimum number of components that must be connected in parallel so that th Probability that the system operateds exceeds 0.9999? The minimun number of components that must be connected in parallel is.
9) A hypothesis test is to be conducted using the claim that the mean hourly wage of employess in a large company is at least $21. What are the null and alternative hypothesis? pick one a H 0 : 21 vs H a : < 21 b H 0 : μ ≤ 21 vs H a : μ > 21 c H 0 : μ 21 vs H a : μ < 21 d H 0 : p 21 vs H a : p < 2
A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts the lot of N₁ + N₂ = 25 bulbs if the number of defectives, X among n = 5 items taken at random and without replacement from the lot is less than or equal to 1. The operating characteristic curve is defined as the probability of accepting the lot, namely OC (p) = P(X ≤ 1) = P(X = 0) + P(X = 1), where p = N₁/25 is the probability of a bulb being defective. (a) Show that the probability of the picking exactly X defectives follows a hypergeometric distribution. (b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 and p = 0.16. (c) Plot, using R, the operating characteristic curve for N₁ = 1 to N₁ = 4.
Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
Suppose that independent Bernoulli trials with parameter p are performed successively. Let N be the number of trials until x successes, and X be the number of successes in the first n trials. Show that P(N = n) = "P(X = x).
A.2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter lambda. a) If X1, X2. ..., Xp are the times, in minutes, between Successive customers selected randomly, estimate the parameter of the distribution. b) The randomly selected 15 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, 1.8, 0.9, 1.5 and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.4 error and 4% risk, find the minimum sample size.
There are 2 players in a game. Each player independently picks a real number on the interval [0, 1] uniformly. If the (absolute) difference between the two numbers is less than a (0 < a < 1) and the sum of the two numbers is less than 1, then both players win, otherwise both players lose. What is the probability of winning? 2.
An electronics store has received a shipment of 20 table radios that have connections for an iPod or iPhone. Ten of these have two slots (so they can accommodate both devices), and the other ten have a single slot. Suppose that six of the 20 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (a) What kind of distribution does X have (name and values of all parameters)? O hypergeometric with N = 10, M = 6, and n = 10 O binomial with n = 20, x = 10, and p = 6/20 hypergeometric with N = 20, M = 10, and n = 6 O binomial with n = 10, x = 6, and p = 6/10 (b) Compute P(X= 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) P(X = 2) = P(X ≤ 2) = P(X ≥ 2) = (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.) mean value standard deviation…
12. Let X be the number of successful rocket launches in 629 independent trials with success probability 0.894. Using the binomial distribution, let Q₁ the probability that X ≥ 542, Q₂ the probability that X ≤ 572, and Q3 the probability that 558 ≤X ≤ 572. Let Q=In(3 + |Q1| +2|Q2|+3|Q3|). Then T = 5 sin² (100Q) satisfies:- (A) 0 ≤T < 1. (B) 1 ≤ T <2. — (C) 2 ≤T < 3. — (D) 3 ≤ T < 4. (E) 4 ≤ T ≤ 5.
Solve all plz
the second photo is an example of resolution
Calculate the following probabilities. a) If X,X-NID(-0,0¹), what is approximate value of Pr(-Sa')? e) If X₁ X₂X₁-Noa), K.,.,- N(0,0)), and Xs and Ys are independent, what T (L.) is Pr X₁-X ox

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