In each of the following cases, give an algorithm that uses exactly one random number of...
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose pdf and cdf are given by f(y) = (1/0)e¬y/® and F(y) =1 – e-y/0, 0 > 0. It is also known that E[Y;] = 0. ', y > 0, respectively, with some unknown (a) Let X = min{Y1,Y2, Y3}. Show that X has pdf given by f(æ) = (3/0)e-3y/º. Start by thinking about 1- F(x) = Pr(min{Y1,Y2, Y3} > x) = Pr(Y1 > x,...
This question uses a discrete probability distribution known as the Poisson distribution. A discrete random variable X follows a Poisson distribution with parameter λ if Pr(X = k) = Ake-A ke(0, 1,2, ) k! You are a warrior in Peter Jackson's The Hobbit: Battle of the Five Armies. Because Peter decided to make his battle scenes as legendary as possible, he's decided that the number of orcs that will die with one swing of your sword is Poisson distributed (lid)...
(4) Consider the following random family tree: Let Y, denote the (random) number of people in the nth generation. Each person in the nth generation produces a random number of offspring, which has a Poisson(A) distribution. The total number of such children is then denoted Yn1 The number of offspring produced by any person is (statistically) independent of the number produced by another person. Moreover, Yo 1, that is, there is exactly one person in the zeroth generation. (a) Determine...
Write four overloaded methods called randomize. Each method will return a random number based on the parameters that it receives: randomize() - Returns a random int between min and max inclusive. Must have two int parameters. randomize() - Returns a random int between 0 and max inclusive. Must have one int parameter. randomize() - Returns a random double between min and max. Must have two double parameters. randomize() - Returns a random double between 0 and max. Must have one...
Rules to follow are:Declare an array with 1000 elements of type intThen in a loop generate 1000 random numbers and assign one to each element in the arrayThe random numbers should be between 1 and 50do not use rand or srand, use code is providedThen, prompt the user to enter a number, store this number in a local variable, the number should be safety checked using the GetInteger() functionThen, iterate through the array and determine how many times the user's...
: Let Yi, ½' . . . , Yn be an iid random sample from an exponential distribution with parameter where θ > 0. Here each Y, represents the lifetime of the ith battery, while θ represents the theoretical average lifetime. The pdf of each Y, is therefore given by fy (y) ei-1,2,...,n Consider the empirical average lifetime of the sample of n batteries given by Let a E R be a nonnegative real number. Consider the event A, defined...
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...
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3. Discrete Random Variables You have a biased die, where the probability that a number n appears on the die when it is rolled is defined as a random variable X such that Р(X %3D п) — с:п Here c is a positive real number. Now answer the questions below: (a) Find the value of c (b) What is the expected value of the random variable X? (c) Find how close a number you...
In each of the summer months (June, July, August), the number of accidents per months at a busy intersection is Poisson distributed with mean 1.5 accidents/month. For all other months, the number of accidents is Poisson distributed with mean 0.5 accidents/month. 7. a) (3 pts) First, let Y an, YFeb, YMar,... be the number of accidents occurring in the months of January, February, March, etc. Define a variable A- the total number of accidents occurring in the second half of...
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Part 1. (6 points) Identify the distribution For each random variable: State the distribution that will best model random variable. Choose from the common distributions: Uniform, Exponential or Normal distribution. Explain your reasoning. State the parameter values that describe the distribution. Give the probability density function. a. b. c. Random Variable 1 A statistics student has a part time job as a coffee shop barista, she realizes the time between customer orders is a random...