Assume the time required to fully recharge an electric car is uniformly distributed between 160 and 220 minutes. What is the expected charge time, E(x)?
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Assume the time required to fully recharge an electric car is uniformly distributed between 160 and 220 minutes.
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What is the expected charge time, E(x)?
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- a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?What is the Marginal PDF of f(x)=2? Is the event independent?
- Consider a cohort of patients receiving an experimental two-year treatment for a serious disease. Suppose that only 20% of the patients survive to the end of the second year. Assume CFM (constant force of mortality) within each year of treatment. Find the probability that a patient who survives the first four months dies by the end of the 20th month. Round to 4 decimal places.A study of the isopluvial maps revealed that at Najaf Al-Ashraf a maximum rainfall depth of 175 mm in 18 hr has a return period of 100 years. The probability of an 18 hr rainfall equal to or greater than 175 mm occurring at Najaf Al-Ashraf at least once in 50 years isIf Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?
- What is the dirac delta "spike" function defined as?If X is a random variable that is uniformly distributed between -1 to 1, find the PDF √|X| of and pdf of -ln|X|Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
- If X = ln Y has a normal distribution with the mean μand the standard deviation σ, find the probability densityof Y which is said to have the log-normal distribution.If X has an exponential distribution with the param-eter θ, use the distribution function technique to find the probability density of the random variableY = ln X.Suppose X and Y are independent, exponentially distributed random variables with rate parameter λ, λ > 0. Find the joint PDF of U and V , where U = X + Y, V = X/Y.