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- The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fyx=x(y) = C (x²-y²) x° e Ex, for -xLet 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?For the joint probability density function f(x.y)= k(x² +y²), -2Choose a point uniformly at random in the unit square (square of side length one). Let D be the distance of the point chosen to the nearest edge of the square. (a) Compute P{D > 0.37}. (b) Let fo denote the probability density function of D. Evaluate fp(0.25). (c) Calculate E[D].Consider the following exponential probability density function. f(æ) = e for x>0 a. Which. of the following is the formula for P(x 4) (to 4 decimals). d. Find P(x < 5) (to 4 decimals). e. Find P(2 < x < 5) (to 4 decimals).Suppose X has probability density function fx (x) =e for x > 0 and fx (x) = 0 otherwise . Р(2 < X<7) —?[Q1] If the probability density function is f(x) as follows, find: (a) k that makes f(x) a valid pdf, (b) Var(x). Skx*(1- x) 0a.71/36 b.71/9 c.287/72 d.179/36 e.71/144B. Consider the probability density function f(x) = kxe³x 1Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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