The probability density function for the continuous random variable X is given by: (A(x² – 2x + 21) 0
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- Sketch the graph of the probability density function over the indicated interval and find the indicated probabilities. f(x)= (3/16 √x) [0,4] A)P(0<x<2)B)P(2<x<4)C)p(1<x<3)D)P(x≤3)The distribution function of the random variable X isgiven byF(x) = 1 − (1 + x)e−x for x > 00 for x F 0Find P(X F 2),P(1 < X < 3), and P(X > 4).Q1. The cumulative distribution function of the random variable X is F(x) = 0, (x+1)², 1- (1-2)², 1, for x 1 (a) Compute-P(0.5 < X <1)¶ (b) What is the probability density function of X.?
- Let X be a continuous random variable with cdf F(x). Show that E(I(X < x)) = F(r) where I is the indicator function (1 if XThe probability density function for the continuous random variable X is given by: (А(х? — 2х + 21) 0The probability that none of the three bulbs in a set of traffic lights will have to be replaced during the first 1200 hours of operation if the lifetime X of a bulb (in thousands of hours) is a random variable with probability density function f(x) = 6[0.25-(x-1.5)2] when 1 ≤ x ≤ 2 and f(x) = 0 otherwise isRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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