ii) Find the power of the test which rejects H, if Y> 1.
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2.STATISTICAL INFERENCE
Question 4 a ii)
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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.Let Y be a continuous random variable with cumulative distribution function: A A B B C C D D E E F(y) = 1-e-(y-a)², where a is a constant. What is the 75th percentile of Y? (A) F(0.75) (B) -√2 In ¹ √2 In ¹ (C) (D) a - 2 Vln2 (E) a +2√In2 a- a + for y ≤ a otherwiseThe pH water samples from a specific lake is a random variable X with probability density function. f(x) = {8 (7– x)², 5 < x<7 0, elsewhere a. ) Find E(X) ( expected value or mean) b. ) Find V(X) ( Variance)
- C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?The random variable x follows a uniform probability distribution in the interval (0,1); the probability of obtaining x values outside this range is zero. What is the probability distribution of y = ln x?
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