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- Consider the random variable with a probability density function of f(x)= (1/x ln(1.5)), 4<=x<=6 and f(x) = 0 elsewhere. What is the expected value of this random variable? What is the median of this random variable?The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density functionA continuous random variable has the probability density function f(x) = 1/8 for 0 ≤ x ≤ 8. What is the expected value of X?
- What is the expected value of a continuous random variable X with probability density function (pdf) given by f(x) = 2x, 0 < x < 1?First a point is X selected at random from the interval (0,1). Then another point is selected at random from the interval (x,1) in such a way so that x+y>=1. Find the probability density function of ySuppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.
- (a) A lamp has two bulbs, each of a type with average lifetime 1300 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean ? = 1300, find the probability that both of the lamp's bulbs fail within 1500 hours. (Round your answer to four decimal places.) (b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1500 hours. (Round your answer to four decimal places.)2. If the probability density function of a random variable is given by f(x0=sinh 2x 1≤ x ≤ 2 a) Find the mean b) Find the total area c) Illustrate the graphCombined probability density function of continuous random variables X and Y -∞<x<∞ , -∞<y<∞ If it is assumed to be defined in the range, which of the following is / are true?
- The probability density function of the random variable X is as in the picture with λ> 0. Find the moments estimator (λ^) of the parameter λ.Can you show an example of what Fundamentals of probability: Cumulative Density Function How is this used in math?(a) A lamp has two bulbs, each of a type with average lifetime 1800 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1800, find the probability that both of the lamp's bulbs fail within 1800 hours. (Round your answer to four decimal places.)(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1800 hours. (Round your answer to four decimal places.)
