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- Solve asapOne of the important properties of the probability density function , f(x) , of a random variable X is f(x) >= 0 , for all values of X. A) true B) falseA lamp has two light bulbs with an average lifespan of 1400 hours. Assuming we can model the probability of failure of these bulbs by an exponential density function with mean = 1400, find the probability that both of the lamp's bulbs fail within 800 hours.
- How do you check if your joint probability mass function is correct?If X ~ U(3, 15), what is the probability density function for this distribution?The time it takes me to wash the dishes is uniformly distributed between 12 minutes and 22 minutes. The probability density function is f(x)=110f(x)=110.What is the probability that washing dishes tonight will take me between 13 and 20 minutes?Give your answer accurate to two decimal places.
- The probability density function is f(x) = c(1-x^2 ) -1<x<1 Find interquartile range.The values of a and B O Directly Proportional always add up to 1.0 are the probability of Type I error Inversely ProportionalThe life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772
- Defects occur along the length of cable at an average of 5 defects per 4,000 feet. Assume that the probability of k defects int feet of cable is given by the probability mass function: e -(5t/ 4000) ( 5 t/ 4,000 ) k P(k defects ) = k ! for k = 0, 1, 2, .. Find the probability that a .... 3,200 foot cable will have а. at most three defects b. at least four defects С. between 1 to 5 (inclusive) defectsThe probability density function of the 'x' continuous chance variable is as shown in the figure. So what is P (X> 30)?A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tons
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