For a particular kind of battery, the probability density function for x hours to be the life of a battery selected at random is given by -x/60 x > 0 f(x) = - 60 0, x < 0 Find the probability that the life of a battery selected at random will be between 15 and 25 hours.
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.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 life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2 for x in [0,∞). Find the probability that a randomly selected laptop battery will last between 2 and 5 years?
- suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?From the density below the probability that X is at least 0.34 is what?
- In a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have a probability density function f(t) = 8 t 2 , t ≥ 8 where 8 seconds is the minimum time to traverse the maze. (a) Find the probability that an animal chosen at random takes between 28 and 56 seconds. (b) Find the probability that an animal chosen at random takes more than 28 seconds given that it took less than 56 seconds.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. What is the probability that the air temperature will be less than 20˚C (so X ≤ 0.5) and it will take no more than 0.2 minute for the engine to warm up?let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a client by answering phone calls, suppose that x has probability density function defin by f(x)=3x^2 for 0< x < 1. find the mean and variance of x
- Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.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, ∞].Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx2; [-1, 2]