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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.If a random variable X ∼ Exponential(1). Find the distribution of Y = X/λ.Suppose the lengths of human pregnancies are normally distributed with u = 266 days and 0 = 16 days. The area to the left of X = 245 is 0.0947. What is the probability that a randomly selected human pregnancy lasts
- Suppose that the distribution of the lifespan of an item has the hazard rate function λ(t) = t3. What is the probability that: (a) the item survives to age 2? (b) a 1-year-old item will survive to age 2?If X is a continuous random variable, what is the value of X that will be exceeded 30% of the time, if 1. X is exponentially distributed with a variance of 1? 2. X has a chi-squared distribution with mean of 10?Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by (1-e-x², x ≥ 0 ={1,- x<0 Find the probability that the random variable X falls within one standard deviation of its mean. Fx (x) =
- 5. Assume = 0.06 and let the force of mortality be given by 0.04, 0 < t < 20 { 0.05, 20Suppose that during rainy season on a tropical island the length of theshower has an exponential distribution, with parameter λ = 2, time beingmeasured in minutes. What is the probability that a shower will last morethan three minutes? If a shower has already lasted for 2 minutes, what is theprobability that it will last for at least one more minute?6. The magnitude (Richter scale) of earthquake along a Taiwanese fault is exponentially distributed, with A= (1/2.5). What is the probability of an earthquake exceeding magnitude 6.4? There is 1 earthquake per year (on average) along the fault with magnitude greater than 5.5. Given this, what is the probability of an earthquake during the year that exceeds magnitude 7.2?7. A pumping station operator observes that the demand for water at a certain hour of the day can be modelled as an exponential random variable with a mean of 100 çfs (cubic feet per second). а. Find the probability that the demand will exceed 200cfs on a randomly selected day. b. What is the maximum water-producing capacity that the station should keep on line for this hour so that the demand will exceed this production capacity with a probability of only 0.01?22. The life X in months of a certain light bulb is a random variable with exponential density. What is the probability that the light bulb will have a life span between 25 and 30 months if its average life is 20 months?.If the variance of a Poison variate is 3. Find the probability that, ne. (1) X = 0 (ii) 1sx<4 eor (iii) 0SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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