Please show solutions for a to e 21. The error in the length of a part...
Question 3 (10 point) The error in the length of a part (absolute value of the difference between the actual length and the target length), in mm, is a random variable with probability density function 0 otherwise a. Find the cumulative distribution function of the error b. What is the probability that the error is less than 0.2 mm? c. Find the mean error d. Find the variance of the error. e. The specification for the error is 0 to...
The diameter of a rivet (in mm) is a random variable with probability density function ?(?) = { 3 4 (? − 9)(11 − ?) 9 < ? ≤ 11 0 ??ℎ?????? } a. find the cumulative distribution function of the diameter b. the specification of the diameter is 9.4 to 10.2. what is the probability the specification is met
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
2- 5. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. Let B>0, 8>0. Consider the probability density function x>0 zero otherwise Recall (Homework #1) V-Χδ has an Exponential(8-T )-Gamma(u-l,e-1 ) distribution. Let X1, . , X/ be a random sample from the above probability distribution. y-ΣΧ.Σν i has a Gamma(u-n, θ- 1 ) distribution. !!! i-l 2. suppose δ is known. Let Xi, X2, , Xn be a random sample from the distribution with...
A shop produces pipes of 100cm length. But due to manufacturing errors, sometimes the pipes are too long or too short. Let X be the error in the length of pipes produced in a shop. X has the following probability distribution f(x)= SA(1 – x)2 if –1<x<1, 10 otherwise a. Find A. b. Find the cumulative distribution function of X? c. Find the expected value of X. d. Find the variance of X. e. What is the probability that a...
1. A shop produces pipes of 100cm length. But due to manufacturing errors, sometimes the pipes are too long or too short. Let X be the error in the length of pipes produced in a shop. X has the following probability distribution f(x)= A(1 - x)? if -1<x<1, otherwise a. Find A. b. Find the cumulative distribution function of X? c. Find the expected value of X. d. Find the variance of X. e. What is the probability that a...
Problem 5. The joint density of X and Y is given by e" (z+y) fx.-otherwise. İf 0 < x < oo, 0 < y < 00, Consider the random variable Z-; a) Find the cumulative distribution function of Z b) What is the probability density function of Z?
s(x)={44 A shop produces pipes of 100cm length. But due to manufacturing errors, sometimes the pipes are too long or too short. Let X be the error in the length of pipes produced in a shop. X has the following probability distribution ŞA(1 – x){if -3<x<3, otherwise a. Find A. b. Find the cumulative distribution function of X? c. Find the expected value of X. d. Find the variance of X. e. What is the probability that a pipe is...
Let X be a random variable with probability density function (pdf) given by fx(r0)o elsewhere where θ 0 is an unknown parameter. (a) Find the cumulative distribution function (cdf) for the random variable Y = θ and identify the distribution. Let X1,X2, . . . , Xn be a random sample of size n 〉 2 from fx (x10). (b) Find the maximum likelihood estimator, Ỗmle, for θ (c.) Find the Uniform Minimum Variance Unbiased Estimator (UMVUE), Bumvue, for 0...