6. A continuous random variable X that can assume values between x-1 and x-4 has a density function given by f(x) = 1/3. a. show that the area under the curve is equal to 1. b. find P(1.5 2)
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- 1. UNIFORM DISTRIBUTION The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function: {' .075x + .2 3 < x< 5 f(x) = otherwise a. Graph the pdf and verify that the total area under the den- sity curve is indeed 1. b. Calculate P(X< 4). How does this probability compare to P(X < 4)? c. Calculate P(3.5 < X<4.5) and also P(4.5 < X).6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?Let x denote the amount of time for which a book on 2-hour reserve at a college library is checked out by a student, and suppose that x has density func-tion f(x)=0.5x for 0<x<2 mean: 1.33 meadian: 1.41 What proportion of checkout times are within one-half hour of the mean time? What propor-tion are within one-half hour of the median time? NOTE: answers are 0.615 & 0. 707 but I am not getting it right
- 3. Given two independent random variables X and Y with a uniform distribution between [2,5]. If Z = min(X, Y) and W = max(X, Y) a.Determine the density function f(z) b.Determine the density function f(w). C.Determine the density function f(z, w)please do this typewritten asap.5. A continuous random variable X that can assume value between x-2 and x-5 has a density function given by 1+x f(x) = 8 a. Show that P(21. Let X be a continuous random variable with the following density function: cx,09. Let X be a random variable with density function f and characteristic function p. Show, subject to an appropriate condition on f, that [ f(x)² dx = 12/16 (1) 1² dr. 276. The random variable X is distributed by f(z)=e, z>0. What is the density, g(y), of where it is non-zero? A. 1 X²¹ 2y³/2 B. 2√9 C. 29-√7 D). -1/47 -1/ E. e5. Let X be a random variable whose density is given by the formula cx? if x E (0, 2) f (x) = otherwise. (a) Find c. (b) Let Y be the integer part of X, i.e., Y = 0 if 0 < X < 1 and Y = 1 if 1I need help with this3.18 A continuous random variable X that can as- 5 has a density sume values between x = 2 and x = function given by f(x) = 2(1+x)/27. Find (a) P(X < 4); (b) P(3 ≤ X < 4). 3.19 For the density function of Exercise 3.17, find F(x). Use it to evaluate P(2 < X < 2.5). 3.20 For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 ≤ X < 4).Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON