Math Answers

8. Let (x1, x2, ..., xn) be independent measurements of a random variable X with density function

f(x) = e−(x−α), x > α. Find an estimator, ˆ

α, of α by method of moments.

Sally can paint a room in 8 hours while it takes steve 9 hours to the same room. How long would it take them to paint the room if they worked together?

type an integer or a decimal round to one decimal place as needed

in 205 14.9 out of every 50 employees at a company were women. if there are 43,030 total company employees, estimate the number of women

At what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec

The number of automobile accidents a driver will be involved in during a one-year period is a random variable Y having a Poisson distribution with parameter X, where X depends on the driver. Suppose a driver is chosen at random from some population and hence X itself is a

continuous random variable with p.d.f f(x) , 0 < x < ∞

(a) Show that P(Y=k)= int o ^ infty P(Y=k|X=x)f(x)dx

(b) Suppose that x has an exponential distribution with mean 1/c where c is a

positive constant. Obtain the distribution of Y, hence find the expectation of Y.

The random variable X_{1} , X 2 ,.......,Xn , are independent and each has a poisson distribution with mean 1. Let Y=X 1 +X 2 +........+Xn . find the conditional distribution of X mathcal N given Y.

Consider Y, the number of successes in Mindependent Bernoulli trials each with success

probability X. Suppose that X itself is a r.v which is uniformly distributed over (1, 0)

(a) Find the p.m.f of Y and identify the distribution

(b) What is the mean and variance of Y.

The number of eggs X laid by an insect is known to have a binomial distribution with

parameter n and p.(0<p<1) . Each egg laid has a probability of hatching independently

of the development of any other eggs.

(a) Show that the number of eggs hatched has a binomial distribution

(b) What does this mean?

(c) What is the mean and variance of the number of eggs hatched?

An operation manager in charge of a company's manufacturing keeps track of the number of LED television in a day. Compute for the following data that represents the number of the LED television manufactured for the past three (3) weeks: 20,18,19,25,20,21,20,25,30,29,28,29,25,25,27,26,22. a. Construct frequency distribution (frequency,cumulative frequency, class boundaries and midpoint). In determining the classes of the data you will use (Rules #1). b. Compute for the mean,median and mode of the data using grouped data. c. Construct a stem and leaf of the data.

Given a sample of 100 projector bulbs from a company has a mean

length of life of 20.5 hours with a standard deviation of 1.6 hours, how do I find a 95% confidence interval for the average length of life of those bulbs and then interpret the results?