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- Which of the following validates a probability density function?* all f(x) must be greater than or equal to 0 all f(x) must be less than or equal to 1 the integral of the probability density function must be equal to 1 from its lower limit to its upper limit the sum of the probabilities of f(x) must be equal to 1 all of the choicesI need the answer as soon as possibleThe probability density function is f(x) = c(1-x^2 ) -1<x<1 Find interquartile range.
- Show that the standard normal probability density function f(x) has points of inflection when x = ±1.11. Let X be a continuous random variable with probability density function r>0 f(x)= 0, otherwise, where 1> 0. Let Y be the largest integer less than or equal to X. Determine the probability function of Y.a) Let X be a continuous random variable with the following probability density function (2x3 f(x)={11 2 +5) , 0A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density functionfx(x) is a probability density function such that fx(x) = {a(2 - x) 0 k), please find k. %3D O a. 1+(2/V2) O b. 2+(1//2) O c. 1+(1//2) O d. 2+(3/v2) O e. 2+(2/v2)The time, X, for clearing side effects of water purification, in days, has the following cumulative distribution F: 1 F(x) = 0 for x 9 2 a) What is the probability density function for X for 1 5? c) What is the probability X 7? e) What is the probability that X > 6.3? f) What is the probability that X > 7 given the X > 6.3? g) Calculate the 70th percentile of X. h) What is the expected value of X? i) What is the expected value of x2 ? j) What is the variance of X? k) What is the probability that X is more than 0.1 below its expected value?Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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