a) Find k such that the function is a probability density function over the given interval. b) Then write the probability density function. ƒ(x) = [5, 20] k -, X
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- HW#9Let X be a random variable with probability density function [ a + bx², 0At a restaurant, the density function for the time a customer has to wait before being seated is given by f(t) = 2e¯ if t > 0. Find the probability that a customer will have to wait at least 6 minutes for a table. Probability = .000006 -2t5. Suppose that h(x) f(x) -3x²² h'(−1) = 2, and 3f'(−1) — f(−1) = 31. Find the values of f'(−1) and f(-1). =Letx and be a random variables with probability density function f(xy) = k 0sxsys1 1- Find the constant kсх, f(x)= 0The probability density functionThe probability density of a random variable X is given in the figure below. 1 2. a) Write the density function of X: f(z) = 0Consider a constant function: f(x)= c; a ≤ x ≤ b Suppose that the function represents a probability density function and c<1 , which of the following is true? a. |a−b|<0 b. |a−b|<1 c. |a−b|>1 d. |a−b|=1Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,