here population mean time to repair E(Y) = y*f(y) dy
= (y/4)*e-y/4 dy =(-(y/4)*4*e-y/4 -(1/4)*4*4*e-y/4) |0 =4*e-0 =4 years
6. Based on extensive testing, it is determined by the manufacturer of a washing machine that...
After extensive studies, economists have determined that an average Canadian family can live on their savings for t months, according to the probability density function: f(t) = 0.64te-0.86 t> 0 Calculate the probability that a randomly selected family can live on their savings for: (a) Between 0 and 3 months: P(0<t<3) (b) Longer than 6 months: P(t >6) Write your final answers as decimal values rounded to four decimal places.
3. (4 points) A manufacturer's annual losses follow a distribution with density function: 2.5(0.6)2.5 f(x)235x 0 elsewhere To cover its losses, the manufacturer purchases an insurance policy with an annual deductible of 3. Let Y be the insu payment. a) What is the difference between the median and the 99th percentile of Y? What is the mean of the manufacturer's annual losses not paid by the insurance policy? 3. (4 points) A manufacturer's annual losses follow a distribution with density...
The answer is NOT "To greater than 1.678" A laptop manufacturer has completed extensive testing over a long time and claims that their new computer batteries will last for 4 hours with a std. dev. of 0.2 hours, that the data is normally distributed, and lists this on their spec. sheet. One of their engineering interns took a recent sample of data claims that the mean is greater than that claimed on the spec. sheet based on a single same...
(15 points) A manufacturer is studying the length of time required by a maintenance team to respond to reported failure of a specific machine in the plant. The plant manager wants to know the percentage of repair calls answered within 10 minutes. 2. The response time, X, measured in minutes is known to have an exponential distribution. For the exponential distribution, as λ increases what happens to the mean and variance of the distribution? 4 points) Draw a sketch of...
An auto manufacturer claims that the average length of time that one of its cars is owned before it requires a major repair is at least seven years. Assume that a survey of ten owners of the manufacture's cars finds that they went an average of 6 years before a major repair and the sample standard deviation for such time lengths was 1.8 years. Use the data to test the manufacture's claim at a 5% significance level. A. Give the...
For problems 7 and 8, an auto manufacturer claims that the average length of time that one of its cars is owned before it requires a major repair is at least seven years. Assume that a survey of ten owners of the manufacture's cars finds that they went an average of 6 years before a major repair and the sample standard deviation for such time lengths was 1.8 years. Use the data to test the manufacture's claim at a 5%...
For problems 7 and 8, an auto manufacturer claims that the average length of time that one of its cars is owned before it requires a major repair is at least seven years. Assume that a survey of ten owners of the manufacture's cars finds that they went an average of 6 years before a major repair and the sample standard deviation for such time lengths was 1.8 years. Use the data to test the manufacture's claim at a 5%...
Let X and Y have a joint probability density function f(x, y) = 6(1 − y), 0 ≤ x ≤ y ≤ 1, =0, elsewhere. (a) Find the marginal density function for X and Y . (b) E[X], E[Y ], and E[X − 3Y ]
How to get the cdf when y>x>0? Thanks 6. The joint probability density function (pdf) of (X, Y) is given by 0y<oo, elsewhere. fxr, y) (a) Find the cumulative distribution function of (X, Y) (b) Evaluate P(Y < X2) (c) Derive the pdf of X and then compute the mean and variance of X (d) Find the pdf of Y and compute the mean and variance of Y (e) Calculate the conditional pdf of Y given X (f) Compute the...
# 6 If two random variables have the joint density f(x, y)=59 y?) for 0<x<1, 0<y<1 0 elsewhere a. Find the probability that 0.2 X<0.5 and 0.4<Y<0.6. b. Find the probability distribution function F(x, y). c. Are x and y independent?