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- The life expectancy (in years) of a certain brand of clock radio is a continuous random variable with the probability density function below. 2/ (x+ 2)? if x20 f(x) = otherwise (A) Find the probability that a randomly selected clock lasts at most 4 years. (B) Find the probability that a randomly selected clock radio lasts from 4 to 9 years. (C) Graph y = f(x) for [0, 9] and show the shaded region for part (A). (A) What is the probability that a clock will last no more than 4 years? (Type a decimal rounded to three decimal places as needed.) 3 DEA 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?(1) Let X b(16,- 5,-) find E(4- 3x) and distribution function.
- Suppose that an item has a hazard rate function X(t) = 2.4t², t> 0. What is the probability that (a) the item survives to age 0.5? (b) the item's lifetime is between 1.5 and 3? (c) a (-year-old item will survive to age 3?A variable X is distributed at random between the values 0 and 4 and its probability density function is given by: f(x) = kx³ (4- x)². Find the value of k, the mean and standard deviation of the distribution.Please answer all part : Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2). (a) What is the distribution of rt(8) = rt + rt−1 + rt−2 +...+ rt−7? (b) What is the covariance between r7(3) and r9(3)? (c) What is the conditional distribution r17(3) given that r16 =0.004 (d) What is the probability that the gross return over the first 10 times periods is at least 1.05?
- The time (in hours) required to repair a machine is exponentially distributed 1 with parameter 2 = = what is the probability that the repair time exceeds 3 3(3) Let X = b >(8,-) find E(5+6x) and distribution function.21. (a) Explain why the function TTX sin 10 if 0 10 is a probability density function. (b) Find P(X < 4). (c) Calculate the mean. Is the value what you would expect?
- If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.The random variable X has the probability density function 2x, 0The density function of X is -120x- 0, f(x) = (2(x - 1), (a) Find the mean E(4X+3); (b) Find the variance 3x+2. 1 < x < 2, elsewhere.SEE MORE QUESTIONS