ch paper states that the distribution of the daily sea-ice advance/retreat from each sensor uble exponential. The proposed double exponential distribution has density function f(x) estandard deviation is given as 40.9 km. (Round your answers to four decimal places.) is the value of the parameter 2? %3! is the probability that the extent of daily sea-ice change is within 1 standard deviation of t
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- Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5?e−?|x| for −∞ < x < ∞. The standard deviation is given as 41.2 km. a. What is the value of the parameter ?? b. What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value?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?Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5?e−?|x| for −∞ < x < ∞. The standard deviation is given as 40.6 km. (Round your answers to four decimal places.) (b) What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value? Note: 0.4386 is not the answer
- Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would: Have the same height but one would be shifted 4 units to the right. Have no horizontal displacement but one would be flatter than the other. Have no horizontal displacement but one would be steeper that the other.suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that W takes on a value between 0.5 and 1.75? What is E(W)? Suppose that the domain of W changes to 0<t<2.5, what happens to the Probability Density Function (PDF)?
- 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?The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of ?=0.5 per year. Thus, the density of X is:f(x,?) = ? e−?x for 0 ≤ x ≤ ∞, ? = 0.5 . ? is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter ? for the distribution allows you to easily answer parts a ,b ,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts . Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts.a) What is the expected value of X? b) What is the variance of X? c) What is the standard deviation of X? d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 5? f) What is the probability that X is > 10? g) What is the probability that X > 10 given that X > 5? h) What is the median of X?Find (a) the mean of the distribution, (b) the standard deviation of the distribution, and (c) the probability that the random variable is between the mean and 1 standard deviation above the mean The length of time (in years) until a particular radioactive particle decays is a random variable t with probability density function defined by ƒ(t) = 4e-4t for t in [0, ∞].
- Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. While you cannot guess the value of the correlation from the regression curve for X or Y, do they suggest whether it likely is positive or negative?With the known values of a = 200,000 and b = 230,000, the first equation for the probability density function for the sales price of a home is found as follows. f(x) = 1/b – a, a ≤ x ≤ b = 1/230,000 − 200000, 200,000 ≤ x ≤ 230,000 = 1/30000, 200,000 ≤ x ≤ 230,000 Everywhere else, the probability density function will just be 0. Therefore, the full probability density function for the sales price of a home follows. f(x) = _______________ 200,000 ≤ x ≤ 230,000 elsewhereThe distance, X, between consecutive anomalies on long cable has an exponential distribution with mean 12 meters. Thus, the density of X is:: f(x,?) = ? e−?x for 0 ≤ x ≤ ∞, ? = 1 12 . ? is what R calls rate.Hint: This is a problem involving the exponential distribution. Knowing the parameter ? for the distribution allows you to easily answer parts a ,b ,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts . Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. ) What is the probability that X is larger than its expected value? e) What is the probability that X is > 13? f) What is the probability that X is > 14? g) What is the probability that X > 14 given that X > 13? h) What is the median of X?