Q.37 A probability density function is of the form p(x) = Kealxl, x e (-0, 0). %3D The value of K is (а) 0.5 (c) 0.5 a (b) 1 (d) a
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- 1. A random variable X has a probability density function given by 2x + 6 fx(x) -3 < x < 2. 25 Let Y = |X|. (a) What is Sy? (b) Is the transformation one-to-one? (c) Derive the cumulative distribution function of Y. (d) Derive the probability density function of Y.S:55)E 6 The random variable Y has a probability density function given by: 1The random variable X has the following probability density function:fX(x)=1/2*e−|x| ,−∞<x<∞ Find E(X) and Var(X)Clearly hand write， As soon as possibleWind engineers have found that wind speed u (in meters per second) at a given location follows a Rayleigh distribution of the type W(v) = 32ve-1²/164 This means that at a given moment in time, the probability that v lies between a and b is equal to the shaded area in the following figure. W 0.1- 0.05 + a graph of W(v) b 20 →v (m/s) (a) Find the probability that v € [0, b]. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of b.)The probability density function of a random variable x is f (x) %3D kx ( х- 1 ) in 1Q.3 The probability density function for a continuous random variable X is fx(x) = {a + bx²; 0Consider the probability distribution function (PDF) f(r) = Ax sin r, for 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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