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    Probability Statistic Problems

    Sample Problems - Please show all your work. QUESTION 1 Suppose that you are working for an energy company that distributes natural gas to residents in a city. As the chief economic analyst, you are asked to analyze the demand for natural gas in your city. Let X denote the random monthly demand for natural gas in millions of


    1) Records show that 30% of all patients admitted to a medical clinic fail to pay their bills and that eventually the bills are forgiven. Suppose n = 4 new patients represent a random selection from the large set of prospective patients served by the clinic. Find these probabilities: a) All the patients' bills will eventually h

    Basic Probability Problems

    1) A shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment, but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24 hour period, what is the expected gain per

    Normal Probability Distribution.

    The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let's interpret this to mean that 95 percent of the flights are cleared in 45 minutes, so 5 percent of the flights take longer to clear. Let's also assume that the distribution is approximately normal. a) If the standard dev

    Marginal Distribution for Random Variable

    Let X1 and X2 be two independent random variables having Poisson Dist. with parameters mew(subscript1)=2 and mew(subscript 2)=3 respectively. Then the marginal distribution for the random variable X2 is : a.) h(X2) = e^-2*2^Xz/X2!, x2=0,1,2,3,... b.) h(X2) = e^-5*5^Xz/X2!, x2=0,1,2,3,... c.) h(X2) = e^-3*3^Xz/X2!, x2

    Cumulative Distribution Function #2

    A lifespan in hours for an electrical component is a random variable x, with cumulative dist. funct.: F(x) = {1-e^-x/100 for x>0 0 elsewhere Determine probability function x for x: Which of the Following Answers: a.) F(x) = {100e^-x/100 for x>0 0 elsewhere b.) F(x) = {1-1/100

    Probability for Construction Projects

    I.) The number of construction projects on a college campus follows Poissan's dist. with a mean=3. The probability that exactly two projects are currently taking place is: 1.) 0.4230 2.) 0.224 3.) 0.00 4.) 0.1990 J.) In an assembly line with robots, a particular component can be installed in 90 seconds if holes a

    Probability-Multiple Choice for a Rock Crushing Company

    F.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another.

    Moment generating function and Poissan's Dist.

    D.) Suppose X1 and X2 are independent exp. random variables, each with mean data and y=X1 and X2. What is the moment generating function for the random variable y? Which choice below is right: 1.) My = (1-t/beta)^-2 2.) My = (1-t/beta)^2 3.) My = (1-beta*t)^-2 4.) My = (1-beta*t)^2 E.) Let X1 and X2 be two di

    Defective Parts w/o replacement and Group size

    Two separate questions below: A.) A bin contains 20 fuses of which 5 will be defective. If 2 fuses are selected at random without replacement, what is the probability that at most, one is defective?(Please show equation) B.) From a group of 5 men and 6 women, how many committees of size 3 are possible with 2 men and one w

    Statistics Probability and Correlation Assistance in Excel

    If we choose a person at random from this database: i. What is the probability that this person will be female? ii. What is the probability that this person will be between 22 and 49 years old? iii. What is the probability that their overall job satisfaction is 4.7 or lower? b ) If we choose a person at random from this

    Order Statistics Sample Distributions

    Let X1, X2, X3 be random sample from a distribution of the continuous type having pdf f(x)=2x, 0 <x < infinity, 0 elsewhere. Compute the probability that the smallest of X1, X2, X3 exceeds the median of the distribution.

    Statistics: A Coin Toss

    A fair coin is tossed 3 times. Let X be the number of heads on the third tossing and let Y be the total number of heads. Questions: a) Find the joint pdf of X and Y. b) Find the marginal pdf of X. Compute E(x) and V(x) - does X follow classical distribution? c) Find the marginal cdf of Y. Compute E(y) and V(y) - does Y

    Density Function : Median and Quartiles

    The density function of a continuous variable x is given by f(x) =x; 0&#8804;x<1 and f(x) = 2-x; 1&#8804;x<2 a) Find p(1/2&#8804;x&#8804;3/2) b) Find the median and quartiles of this distribution

    Decision Analysis (Project Network)

    A project involving the installation of a computer system comprises eight activities. The following table lists immediate predecessors and activity times (in weeks): {see attachment} 1) Draw a Project Network 2) What are the critical activities 3) What is the expected project completion time.

    Probability for PDF or CDF

    A manufacturer of computer printers claims that only 0.55% of all printers they produce fail out of the factory. As a computer store buyer, you purchase 150 of this company's printers. What is the chance that you get at least one defective printer out of this purchase? P(X is greater than or equal to 1)=____________ pleas

    Determining Probability using the Poisson Distribution Formula

    Assume that the number of Telephone calls arriving in an office during a 15 minute period has a Poisson distribution with mean number of calls equal 5. By using a Poisson Distribution Formula, find the Probability that during a 15minute period, there will be exactly 3 calls.


    A jar contains marbles of different colors: 4 white, 6 black, 6 red, and 4 blue. On two random drawings, without replacement, find the probability that the first is black and the second is white. Assume that the draws are independent.


    Take a deck of cards. A deeck has 52 cards with two major colors(Red and Black), with 26 cards each. Red colors comes in two shapes(heart and diamond), while black color shapes are called clubs and spades. Find the probability of obtaining Red or Queen. That is, find Probability(Red or Queen).

    Probability Calculations for Rolling of Two Dice

    Two dice are rolled. Observe their output space and do the following: a) Probability ( sum of numbers making at most 8) b) Probability ( sum of numbers exceeds 8) c) Probability ( both dice having equal odd numbers) d) Probability ( even numbers on both).

    Probability of an Animal Colony

    The animal colony in the reseach department contains 20 male rats and 30 female rats. Of the 20 males, 15 are white and 5 spotted. Of the 30 females, 15 are white, and 15 are spotted. Suppose that you randomly select 1 rate from this colony: a)Find the Joint probability table including the marginal probability. b) what is th

    Probability of a Container Containing a Certain Weight

    The weight of the food packed in certain containers is a normally distributed random variable with a mean weight of 400 pounds and the standard deviation of 4 pounds. Suppose that the container is picked at random. Find the probability that it contains: a) more than 410 pounds b) less than 398 pounds c) between 391 and 398

    Probability problem...

    How many ways can 6 distinguishable balls be placed in 5 boxes such that there are 2 balls in the first box, and one in all remaining boxes?

    Probability bounds using Chebychev's inequality

    Many people believe that the daily charge of a price of a company's stock on the stock market is a random variable with mean 0 and variance {see attachment}. That is, if Yn represents the price of the stock on the n-th day, then (see equation in attachment( where X1,X2,..., are independent and identically distributed random var

    Normal Probability Distributions

    Suppose the lifetime income of all high school grads is normally distributed and that the lifetime income of all college grads is normally distributed. Suppose that the difference in the means is known to be $600,000 and that the standard deviation of the high school graduates is $300,000 and the standard deviation of the colle

    Probability for the Skateworld Company

    The Skateworld Company operates ice rinks in several major cities throughout the United States. During each session of open skating, one customer is selected at random to receive a free pass for a future open skating session. At a recent session there were 150 males and 130 females skating. What is the probability that the pe

    Continuous Random Variables Independent Factors

    Let X1,X2... be a sequence of independent and identically distributed continuous random variables. Define the random variable ... (a) Compute the p.m.f of N by first computing P(N [less than or equal to] n) (b) Show that E(N)=e *(Please see attachement for complete problem)

    Random number sets

    1. Choose a number at random from the set of numbers from the set of numbers {1,2,3,4,5}. Now choose a number from the subset {1,...,X). Call this second number Y. a) Find the joint p.m.f. of X and Y b) Find the conditional mass function of X given that Y = i. Do it for i = 1,2,3,4,5 c) Are X and Y independent? Why?