1. Find the value of c so that the function defined as f(x) = Sce-2x if 0 ≤ x < ∞ otherwise is a probability density function. Determine the probability P(X ≥ 7) 3. Determine the expectation of the random variable whose density function is given in problem 1. 4. Determine the variance of the random variable whose density function is given in problem 1.
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- If a probability density function for X is f(x) define F(x) over the whole real line. = 2(x+1)² for 0 < x < 2, find F(x). Make sure youLet X be a continuous random variable whose probability density function is: f(x)- 1.5x2 for -1Find the value of k that makes the given function a probability density function on the specified interval. f(x) = kx 2 ≤ x ≤ 6 k= || =i. A valid probability density function satisfies 0 ≤ fx(x) ≤ 12. Let X be a continuous variable with probability density function f(x) = cx defined for 0Let f(x) = 0.006x(10-x) for 0 ≤ x ≤ 10 and f(x) = 0 for all other values of x. a. Verify that f is a probability density function. b. Find P(4 ≤ x ≤ 8).Let X be a continuous random variable whose probability density function is given by the formula if 0Let X be a random variable with probability density function 3 f(x) = ,a², –1 < = <1 2 Which of the following is the probability density function of Y = X – 1?Sketch the graph of the probability density function over the indicated interval. F(x) = 1/20, [0, 20] Find the indicated probabilities. a) P(0 < x < 12) b) P(8 < x < 12) c) P(13 < x < 20) d) P(x ≥ 5)= { 2 x3 x > 1 is the probability density function of the continuous c. Suppose g(x) x < 1 random variable X. Find the probability that X ≤4, given that X ≥ 2.The score of a student on a certain exam is going to be a number between0 and 1. Think of it as the percentage of correct answers on the exam. Suppose the student passes the exam if their score Sis at least 0.60 and fails otherwise. If the probability density function of a student score S is given by 4x f(a) = 4 4x3. Find the value of k so that f(x) for 1 < x < 2 is a probability density function. (x + 1)?SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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