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We have twelve balls, four of which are white and eight are black. three blindfolded players, a, b, and c draw a ball in turn, first a, then b, then c. the winner is the one who first draws a white
Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal distribution, and the three times are independent of one another.
Find the p-value for each of these situations, taking into account whether the test is one-sided or two-sided.
There are 46 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random
The third door leads to a tunnel that will return him to the mine after 7 hours. If we assume that the miner is at all times equally likely to choose any one of the doors, what is the moment generat
What is the probability that the coin flipped on the third day after the initial flip is coin 2? Suppose that the coin flipped on Tuesday comes up tail. What is the probability that the coin flipped
Explain how this system may be analyzed by using a Markov chain. How many states are needed? Calculate its transition probability matrix.
A fair coin is tossed repeatedly until a head appears. Let N be the number of trials until the first head appears. Then a fair die is rolled N times. Let X be the number of times that the die comes
However, the owner is concerned his staff isn't following this rule. To make sure they are, the owner decides to count the number of pieces of salmon on the next 40 pizzas and finds the average amou
Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Service goals dictate that an arriving customer should not wait for servic
How significant are the results? What range of p-values would it fall under? Calculate a 95% confidence interval and interpret the results.
If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?
Show that if T has exponential distribution with rate lambda, then int(T), the greatest integer less than or equal to T, has a geometric (p) distribution on {0,1,2,3,...} and find p in terms of lamb
A small town has 100 people in it. 45 of them are men and 55 are women. It is also known that there are 48 Democrats in the town and 52 Republicans. We do not know how many of the women are Republic
Give a point estimate for the proportion of all households in which there is no telephone service of either kind. Assuming the sample is sufficiently large, construct a 99.9% confidence interval for
Suppose that the random variable X representing the probability that a random college student voted in the last student body election has the density function f(x) = kx^2(1-x)I(0,12)(x).
Two cards are selected in sequence from a standard deck of 52 cards. If the first card is 7 what is the probability that the second card is a Spade? Assume the first card is NOT returned to the deck
How low does the concentration of isoamyl acetate in Taipan Light have to be to ensure that less than 10% of people taste the banana flavor?
(Hint: (sigma) iP(X > i) = sigma i(sigma P(X = k)) Now interchange the order of summation and proceed.) sigma) is supposed to be sigma, from i=1 to infinity. > is greater than or equal to
Suppose that X is a continuous random variable with density function given by f(x) = (3/4)(1-x^2)I(-1,1)(x). Obtain the cdf of X, and calculate its mean and variance.
suppose that the random variable X representing the probability that a random college student voted in the last student body election has the density function f(x) = kx^2(1-x)I(0,12)(x). A) show tha
Find the value k for which the function f(x) = kxe^-x^2I(0, infinity)(x) is a valid probability density function
It is estimated that 3.3 million Canadians have diabetes. 90% of all people with diabetes have type 2 diabetes. 90% of people with type 2 diabetes are overweight. What percentage of Canadians have t
Use the inclusion-exclusion principle from the last homework to show that the number of surjections from Nm to Nn is given by n^m - (n choose 1)((n-1)^m) + ... + ((-1)^n-1)(n chooce n-1)(1^m)
If scores on a test are normally distributed, the average score is 120 with a standard deviation of 5. Which percentage of group scored between 112 and 123?