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blocks of bernoulli trialsin n m independent bernoulli p trials let sn be the number of successes in the first n trials
grouping multinomial categories suppose that counts n1 nm are the rum-bets of results in m categories in n repeated
a box contains 2n balls of n different colors with 2 of each color balls are picked at random from the box with
retirement agefrom time to time the telegraph takes random samples from the uk population one such survey is the old
in a world series terms a and b play until one team has won four games assume that each game played is won by team a
sale of air conditionersthe average number of air conditioners sold in 2015 was 3600 per day in a city and that was
let x and y be independent each uniformly distributed on 1 2 n finda px y b px lt y c pxgtyb pmaxx y k for 1 k
sale of microwaves the average number of microwaves sold in 2015 was 2700 per day in the same city and that was larger
let x be the number of heads in 20 fair coin tosses y a number picked uniformly at random from 0 1 nbsp 20
babies weightssome sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard
three dice are rolleda what is the probability that the total number of spots showing is 11 or moreb find a number m
pairwise independence let x1 xn be a sequence of random variables suppose that xi xi and xj are independent for
babies weightsagain some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a
suppose a box contains tickets each labeled by an integer let x y and z be the results of draws at random with
suppose that 10 of the numbers in a list are 1520 of the numbers are 25 and the remaining numbers are 50 what is the
one list of 100 numbers contains 20 ones and 80 twos a second list of 100 numbers contains 50 threes and 50 fives a
sale of air conditioners the average number of air conditioners sold in 2015 in a city was 3600 per day suppose the
suppose all the numbers in a list of 100 numbers are non-negative and the average of the list is 2 prove that at most
in a game of chuck-a-luck a player can bet 1 on any one of the numbers 1 2 3 4 5 and 6 three dice are rolled if the
let x be number of spades in 7 cards dealt from a well-shuffled deck of 52 cards containing 13 spades find
in a circuit containing n switches the ith switch is closed with probability pi i 1 n let x be the total number of
there are 100 prize tickets among 1000 tickets in a lottery what is the expected number of prize tickets you will get
suppose a fair die is rolled ten times find numerical values for the expectations of each of the following random
a building has 10 floors above the basement if 12 people get into an elevator at the basement and each chooses a floor
aces a standard deck of 52 cards is shuffled and dealt let x1 be the number of cards appearing before the first ace x2