Given the probability density function as below: = { Shx² , (-1sx S 1) 0 , otherwise f(x) Calculate the value of u
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- Consider the probability density function if x 5. Find Pr(X < ) (accurate to 4 decimal places). Select one: O 0.7803 O 0.2603 O 0.9897 O 0.2197Find the value of k for which the given function is a probability density function. f(x) = kekx on [0, 7] kConsider the following exponential probability density function. P(x)=3e4 () == e for x ≥ 0 3 In Excel Write the formula for P(x ≤ xo). In Excel Find P(x ≤2) In Excel Find P(x ≥ 3).
- 2. Let X have the probability density function: 10-12². √x f(x) = a. What is a? b. What is E(X)? C. What is Var(X)? 0, 0≤x≤ a otherwiseLet 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), -2Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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