4. The time needed by athletes in any particular marathon to complete a 1 hour run...
CUIL yuuical HWYUU YUL 1. (12 points; 4, 4, 4) A study has shown that if X is the amount of gasoline sold in a day by a particular gas station, then the probability model of the random variable X can be described by Smx 0<x<5 otherwise i. Solve for m so that f(x) is a pdf. ii. Find the cumulative distribution function (cdf). iii. What is the expected number of gallons of gasoline the gas station can expect to...
Let X be a random variable with pdf S 4x3 0 < x <1 Let Y 0 otherwise f(x) = {41 = = (x + 1)2 (a) Find the CDF of X (b) Find the pdf of Y.
For each of the following functions, (i) find the constant c so that f(x) is a pdf of a random variable x, (ii) find the cdf F(x)-P(XSX), (iii) sketch graphs of the pdf f (x) and the distribution function F(x), and (iv) find μ and σ2. (a) f (x) x3/4, 0 <x<c (b) f (x)-(3/16x-,-c < x c
Three friends, Xena, Yvonne, and Zelda, decide to run the Boston marathon. For each of them the time required to complete the marathon is a continuous random variable uniformly distributed between 4 hours and 6 hours. The running times of all contestants are independent. After the marathon, a one hour long TV show interviews the three friends, with 1/2 of the time devoted to the winner, and 1/3 and 1/6 to the second and third, respectively. You are at home,...
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.
BSP2014 5. Given xe 20 Cr) 0 x<0 i) Show thatAx) is a pdf. ii) Find the cumulative distribution function (CDF) of X 6. The p.d.fof a random variable Y is given by y +1 for2<y<4 v) 0 elsewhere Find i) the value of c ii) P(Y<3.2) iii)P(2.9 < γ< 3.2) 7. The p.d.fof a random variable X is given by elsewhere i) Find P(X<1.5) ii) Find P(0.5 X1.5)
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).