Statistics and Probability Answers

Probability of x=10?

Probability of x=10?

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.

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?

The mean gasoline consumption of 10 cars is 28 liters with a standard

deviation of 1.6 liters. Find the interval estimate using 95% confidence

interval.