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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)Show that there are no values of c such that f(x) = cx can serve as the values of the probability distributionof a random variable with the countably infinite rangex = 1, 2, 3, ...
- 24. Let X1, X2, ., X 100 be a random sample of size 100 from a distribution with density .... f(x) = {0 for æ = 0, 1, 2, .,00 otherwise. What is the probability that X greater than or equal to 1?Let X1 and X2 be discrete random variables with joint probability distribution x1 = 1, 2; x2 = 1, 2, 3, f(x1, x2) = 10, 18 elsewhere. Find the probability distribution of the random variable Y = X1X2.2.) For a continuous random variable X,where c is any one isolated number what is: P(X = c) Hint: For continuous random variables we always calculate things like: P(a10. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf f₂ (ylx) of Y.. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours. d) Given that a Type B bulb fails at 300 hours, find the probability that a Type A bulb lasts longer than 300 hours. e) What is the expected total lifetime of two Type A bulbs and one Type B bulb?Let X1 , X2 , X3 be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The mean and variance of p-hat = 1/n ( X1 + X2 +... Xn ) . E(p-hat)= p Var(p-hat) = p(1-p) / n2.5.5.) The cumulative distribution function F(x) of a random variable X is given by 0, -8Show that, if the random variable X has an F-distribution with ν1 and ν2 degrees of freedom, then Y =1Xhas an F-distribution with ν2 and ν1 degrees of freedom.Suppose that X1, ..., Xn are random variables such that the variance of each variable is 1 and the correlation between each pair of different variables is 1/4. Determine Var (X1 + ...+Xn).3 The median value y of a continuous random variable is that value such that F(y) = 0.5. Find the median value of the random variable in 90.5 = f(y) = 2 25 -Y, 0 ≤ y ≤ 5, elsewhere. 0,SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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