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1)If X and Y are both discrete, show that xPX/Y9x/y)=1 for all y such that pY(y)>0. 10) Suppose X and Y are independent continuous random variables. Show that E[X/Y=y]=E[X] for all y

Coins question

52) (from pg. 52) A coin, having probabiliyt p of landing heads, is flipped until head apears for the rth time. Let N denote the number of flips required. a) Calculate E[X] for the maximum random variable fo Exercise 37. b) Calculate E[X] for X as in Exercise 33. c) Calculate E[X] for X as in Exercise 34.

Probability Questions

30)Let X be a Poisson random variable with parameter (lambda). Show that P {X=i} increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding (lambda). Hint: Consider P{X=i}/P{X=i-1}. 37) Let X1, X2, ...., Xn be independent random variables, each

Binomial Distribution

The manager of a restaurant claims that only 3% of the customers are dissatisfied with the service. If this claim is true, what is the probability that the number of dissatisfied customers, in a random sample of 25 customers will be a) 0 b) at least 1 c) between 1 and 5 inclusive d) greater than 5 e) 25

Calculating the probability from a given situation using combinations.

A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. If a given student knows how to solve 15 of the problems, find the probablility that the student will be able to answer, a. All 10 questions on the exam b. Exactly 8 questions on the exam c. At least 9 questions on the exam

Binomial Distribution

Merican air flight 2705 from N.Y. to San Francisco has seats for 340 passengers. An average of 7% of the people with reservations do not show up so American Air overbooks by accepting 355 reservations for the 340 seats. We can analyze this system by using a binomial distribution with N=355 and P=0.93 (the probability that a boo

Trials and probability

Steps: 2) Find p-hat(R), the proportion of days on which it rained given that it rained the pervious day. 3) Find p-hat (NR) the proportion of days on which it rained given that it did not rain the previous day. 4) Construct confidence intervals for both p-hat(R) and P-Hat(NR) (you can chose level of confidence)

Understanding and calculating probability distribution.

A researcher is studying IQ levels. From past experience she knows the population mean IQ for adults is 110 and the standard deviation is 15. a) If samples of 30 IQs are selected and the sample mean is calculated for each sample, what can be said about the sampling distribution of the sample means, and why? b) If she ta

Determining the probability using binomial distribution.

The Bell telephone co. surveyed an apartment building with 500 units to find out who subscribes to their service. Turns out 70% of the units use Bell's service. Find the probability that less than 340 units are using Bell services so we are looking for: P(X<340) Z= 340-350/10.25=-0.98


A manager must select from among ten persons to fill four job openings. Four of the candidates belong to a minority group. If the four positions are filled at random by the candidates, what is the probability that no minority group member will be selected?

Normal Approximations to Binomial Distributions

A survey of workers in the U.S. found that 2.9% work more than 70 hours per week. You randomly select 10 workers in the U.S. and ask each if he or she works more than 70 hours per week. a)find the probability that at most three people say they work more that 70 hours per week b)find the probability that at least three peopl s


A) A coin is tossed 20 times. Find probability of getting at least 14 heads. B) A die is tossed 20 times. Find probability of getting a "1" two times. C) Three dice are tossed. Find probability that a four shows on exactly two of the dice.

Statistics probabilty

A new component for an airplane is being manufactured. Each has a 70% probability of working properly. A sample of 8 components is sampled. Find probability that: A) all work properly. B) 6 work properly. C) at most 3 work properly. D) at least 1 works properly.

Determining the probability from the given situation.

A certain company relies heavily on phone orders. Suppose past records show that R% of all incoming phone calls to this company are orders from customers. At least how big must R be for you to be at least 90% sure that the first phone order of the day will occur on or before the tenth incoming call of the day?

Independent Trials

Suppose a sequence of independent trials is performed where each trial results in either success or failure. Suppose X=the number of failures before the first success, with p=probability of success on any one trial. (a) Find the expected value of X. Be sure to show in detail how you got your answer. (b) Carefully interpret


A bowl contains R red and W white chips. Suppose N chips are drawn without replacement from the bowl. (a) what is the expected number of red chips among the N drawn? The expected number of white chips? (b) Justify your answers from part(a)


A fair die is rolled until win or loss occurs: For k=1 to 5: if a 6 occurs on the kth roll you win N dollars and game ends; if a number<k occurs you lose $10 and the game ends; otherwise you roll again. For k>5: if a 6 occurs on the kth roll you win N dollars and the game ends; if a number<5 occurs you lose $10 and the gam

Stats Problem

1. The camera department of a large department store sells three different brands of cameras: Proxima, Yakima, and Tetron. Approximately 60% of the cameras sold are Yakimas with Tetrons accounting for 30% of sales and Proxima the remaining 10%. Store records show that approximately ¼ of those who purchase a Yakima return wit

Stats Problem

1. A group of day to day workers can work either 0 hours, eight hours or 12 hours at a pay rate of $9.75 per hour. (The 12 hour day pays regular time for the first eight hours and double time for the remaining four hours.) On any given day there is a 0.2 probability of not working at all, 0.7 probability of working an eight ho


Question 1 Assume that you are the owner of a small business that employs two people on a telephone help desk. Records show that one of the employees is busy taking calls for 40% or the time and the other is busy taking calls 55% of the time: a) What is the probability that when a new call comes in that both of the emp


Please explain why in a two card hand out of a deck of 52 cards the probability of getting 2 consecutive cards is 208/1326, how did you get this?

Simple Statistics Problem

16 wrestlers compete in a competition. If each wrestler has one match with each of the other 15 wrestlers, what is the total number of matches.

The Weight of a Goose Probability

A field biologist grabs geese and weighs them. He finds out that the weights of the geese are normally distributed with a mean of 9 pounds and a standard deviation of 1.3 pounds. What then, is the probability that one of these geese snatched at random will weigh less than 10.5 pounds?