Explore BrainMass



Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let U = (X/m) / (Y/n) a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom). b) Find the density of V = U / (1+U)

Joint Probabilities

Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let T = Z / √ (V/n) Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)


Find the probability for the various situations

New Source, Inc. - Probability

NewSource Inc. uses natural gas in its production-processing operations. Neighboring companies in its upstate Ohio area have successfully drilled for gas on their premises, and NewSource is considering following suit. Their initial expenditure would be drilling, which would cost $80,000. If they strike gas, they would have to

Probability of Events: Sum Rule

Our psychology department received a new statistics text for review. Prof. Smart in his review provided an interesting table of corrections. Type: Alterations: 20%, Spelling 50%, Spelling and alterations: 10%. Assuming that spelling and alterations are the only possible types of corrections, calculate the probability of spot

Calculating probabilities of events

1. What are the steps I need to calculate probability of events occurring? 2. Could you apply these steps to the following example: A fair die is tossed, and the up face is observed. If the face is even, you win $5. Otherwise, you lose $5? What is the probability?

Assigning Probabilities to simple events

When assigning probabilities of two simple events, can we assume that each event is always equally likely to occur and, thus assign .5 to each event? Could you provide an example in your explanation?

Probability Problem

A retail grocer has decided to market organic "health foods" and will purchase a new line of products from each of two suppliers. Unknown to the grocer, the two suppliers are in financial distress. Past experience has shown that, for firms with similar credit histories, the probability that bankruptcy proceedings will be initi

Probability Problem

Saint Paul's Hospital commissioned an independent study to determine if there was a difference between the quality of care provided by hospital-trained nurses and tertiary-trained nurses. Two hundred nurses were rated as either providing Superior Service (S) or Adequate Service (A). The results are as follows: (See attached file

Probability - Orange dealership

The manager of an Orange dealership keeps records on customers visiting the store. Records show that 40% of the people visiting the store are female. Thirty-five percent (35%) of the females visiting the store will buy an Orange. The records also point out that 20% of the males visiting the store will buy an Orange. a) What i

Probability Problem

Suppose used car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 used car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak. I have not been able to get the correct answer.

This job calculates Probability.

A major hat store chain is having a sale on three nationally known brands, A, B and C. Probabilities that Brand A, Brand B or Brand C will not be big sellers are: 0.30, 0.40, and 0.50, respectively. All three brands are manufactured by three independent companies. Calculate the probability that: a. None of the brands will b

Probability is explained.

Two events, A and B are equally likely. The chance that either A or B happens on a given trial of an experiment is 0.70, while the chance that they both happen on a given trial is only 0.40. What is the probability that event A happens?

Normal and Poisson approximation to binomial distribution

In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365. For a given month find: 1) The probability taht

Normal & Poisson approximation to binomial distribution

A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A. By using a suitable approximation to the binomial distribution, calculate the probability of A. The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B. By usin

Normal approximation to binomial distribution

The probability that a patient recovers from a rare blood disease is 0.6. If 100 people are known to have contracted this disease, what is the probability that less than 50 people recovers from this rare blood disease?

Binomial distribution

A hockey team consists of 11 players. It may be assumed that, on every occasion, the probability of any one of the regular members of the team being unavailable for selection is 0.15, independently of all other members. Calculate, giving three significant figures in your answers, the probability that, on a particular occasion,

Poisson approximation to binomial distribution

In a large town, one person in 80, on the average, has blood of type X. a)If 200 blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type X. b)How many donors must be taken at random in order that the probability of including at least one donor


1. A random variable X has the following cumulative distribution function F(x) = { 1 - e^(-(x+1)) -1</ x < oo 0 elsewhere. a) 25% of the time, X exceeds what value? b) Find the moment generating function of X, or Mx(t) c) Using your result in (b


Problem: Chances of recieving a direct hit by a scud missile. A scud carries 113kg of explosive, has blast are of 91m in diameter and that missiles are being lobbed into an area 80km long and 48km wide. Assume that missiles fall randomly on this area. a) What is the probability of being in the blast area of a missile? b)


The distribution of blood types for a population are: 40% typeA 9% type B 49% type O 2% type AB Suppose that the blood types are independent and that both the husband and the wife follow this distribution of blood type. a) If the wife has type B, what is the probability that the husband has type B? b) What is the pr


Brain cancer is a rare disease. In any year there are about 3.1 cases per 100000 od population. Suppose a small medical insurance company has 150000 people on its books. How many claims stemming from brain cancer should the company expect in any year? What is the probability of getting more than 6 claims related to brain c


Suppose that X is a random variable which can possibly choose 1,2,3,4 with probability P(X=i)=ci, where c is a constant. Find c


Samples of size 49 are drawn from a population with a mean of 36 and a standard deviation of 15. What is the probability that the sample mean is less than 33?

Poisson vs. Gaussian distribution

Radiation: The atoms of a radioactive element are randomly disintegrating and emitting alpha particles. The number of alpha particles emitted per second from these atoms during a 30 second period is recorded as follows. 9.38 8.08 8.36 10.44 9.44 8.05 17.78 7.56 14.17 6.73 9.81 4.79 11.98 9.48 6.32 14.

Probability function

A standard die has its faces painted different colors. Faces3,4,6 are red, faces 2 and 5 are black and face 1 is white. a) Find the probability that when the die is rolled, a black or even numbered face shows uppermost. a game is played by rolling the die onvce. If any of the red faces show uppermost, the player wins the