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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?
Assume the incomes of cab drivers are normally distributed. If the average salary is $25,000 and the standard deviation is $2,300, what are the boundaries of the middle 40%?
Describe and explain any similarities or differences between the significance of z-scores in your R output and the significance of the deviance value.
What is the percentile of a person with a serum potassium concentration of 4.05 mEq/L? What serum potassium concentration corresponds to the 91st percentile? What proportion of adults are predicted to
The mean and standard deviation of the age of bank customers with large checking accounts are 44.0 and 6.0, respectively. Assume the age distribution follows a normal distribution. Determine the pro
Toss a fair die twice, and record the numbers. Find the probability that the first number is 3 given that the sum of two numbers is odd.
Let X1 and X2 be continuous random variables with the joint probability density function, fX1,X2(x1,x2), -inf.