Problem 4. The life X, in hours, of a certain device, has a pdf 100 0,...
Problem 4. The life X, in hours, of a certain device, has a pdf 100 , t 100 0, t< 100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
please do them both for high rate Problem 3. Let X be a discrete random variable, with probability distribution P(X x)0.95, P(Xx2) 0.05 Determine X1 and X2 such that E[X] 0 and σ2(X)-7. Problem 4. The life X, in hours, of a certain device, has a pdf 100 x()t2 2 100 0, t<100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
Problem 1 The pdf of X, the lifetime of a certain type of electronic device in hours, is given by if x > 10 10 if x < 10 f(x) = { ift 1. (1 point) Find the constant c that makes the a valid pdf. 2. (1 point) Find P(X > 20) 3. (1 point) Find F(x), i.e. the cummulative distribution of X? 4. (1 point) What is the median value of X?
Thank you! 1) Let X be the life (in hours) of a certain electronic device. The pdf of X is f(x)- e-100, for x ? 0 and 0 otherwise. What is the expected life of this device? 100 2) The density function of coded measurements of the pitch diameter of threads of a fitting is 4 0 elsewhere. Find the expected value of X
9. Let y= X2, where X has the pdf below (a) Find the mean of Y without finding the pdf of Y. (b) Write the pdf of Y:f<v). (c) Find the mean of Y using.ffy), confirming your answer in part (a).
1. Let Xi...., X, be a random sample from a distribution with pdf f(x;0) = 030-11(0 < x < 1), where 0 > 0. Find the maximum likelihood estimator of u = 8/1 b) Find a sufficient statistic and check completeness. (c) Find the UMVUE(uniformly minimum variance unbiased estimator of each of the following : 0,1/0,4 = 0/(1+0).
1. Let Xi...., X, be a random sample from a distribution with pdf f(x;0) = 030-11(0 < x < 1), where 0 > 0. Find the maximum likelihood estimator of u = 8/1 b) Find a sufficient statistic and check completeness. (c) Find the UMVUE(uniformly minimum variance unbiased estimator of each of the following : 0,1/0,4 = 0/(1+0).
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
3. (25 pts) The life X, in hours, of a certain kind of electronic part has a probability density function given by fory 2100 f,(y) o, fory <100 (A) What is the probability that a part will survive 250 hours of operation? (B) Find the expected value of the random variable (C) Find the variance of the random variable if the probability density function is given by y 2100 0, y<100.
PROBLEM 1 Let the joint pdf of (X,Y) be f(x, y)= xe", 0<y<<< a. Compute P(X>Y). b. What is the conditional distribution of X given Y=y? Are X and Y independent? c. Find E(X|Y = y). d. Calculate cov(X,Y).