Suppose there are 25 different types of coupons and suppose that each time one obtains a...
Suppose there are 25 different types of coupons and suppose that each time one obtains a coupon, it is equally likely to be any of the 25 types. Compute the expected number of different types that are contained in a set of 10 coupons.
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Suppose there are 25 different types of coupons and suppose that
each time one obtains a...
Suppose that there are 12 types of coupons and that each time one obtains a coupon, it is, indepe...
Suppose that there are 12 types of coupons and that each time one obtains a coupon, it is, independently of previous selections, equally likely to be any one of the 12 types. One random variable of interest is T, the number of coupons that needs to be collected until one obtains a complete set of at least one of each type. Determine the p.m.f. of T, P(T -n) based on the fact P(T- n) P(T> n-1) P(T> n)
Suppose that...
Q. Given 25 different type of coupons, one coupon is obtained each time. one set obtain...
Q. Given 25 different type of coupons, one coupon is obtained each time. one set obtain 10 coupon. The probability that the type i coupon is not in the set is 24C10/25C10. Is it right? (24C10 => combination) If wrong, please tell me the answer. (i is range 1~25. coupon type index)
4. Suppose you continually collect coupons and that there are two different types of coupon, type...
4. Suppose you continually collect coupons and that there are two different types of coupon, type A and type B. Suppose also that each time a new coupon is obtained it is a type A coupon with probability 1/3 and a type B coupon with probability 2/3, independently of what coupons you have collected so far. Let X be the number of coupons collected until you have at least one coupon of both types. (a) Find the probability mass function...
1. Suppose there are m 2 1 different types of coupons, and a total of n...
1. Suppose there are m 2 1 different types of coupons, and a total of n coupons is to be collected. Each new coupon collected is, independent of the past, a type i coupon with probability i, 1 < i< m. Define for i-1,... ,m, Х,-{ 0, otherwise 1, if at least one type i coupon is among the n collected, type Let X = Xut + x,n. Calculate E(X) and Var(X).
Suppose there are n type of coupons. Each new coupon collected is of type i with...
Suppose there are n type of coupons. Each new coupon collected is of type i with probability Pi, independently of any other collected coupon. Here, D=1 Pi = 1. Suppose k coupons are collected. Let A be the event that there is at least one coupon of type i among the k collected. For i #j, (1) Compute P(A|AU A;) (2) Compute P(A|Aj)
The coupon collector problem calculates the expected number of days it takes to get n different coupons, if one receives one of the n coupons at random each day. The number of days is approximately n(...
The coupon collector problem calculates the expected number of days it takes to get n different coupons, if one receives one of the n coupons at random each day. The number of days is approximately n(0.577 + ln n). Use this to calculate the expected number of TCP connections a random port scan (scanning port numbers 0 through 1023) needs to eventually check all 1,024 well- known port numbers.
Exercise 12.6 At each stage, one can either pay 1 and receive a coupon that is equally likely to be any of n types, or one can stop and receive a final reward of jr if one's current collection of...
Exercise 12.6 At each stage, one can either pay 1 and receive a coupon that is equally likely to be any of n types, or one can stop and receive a final reward of jr if one's current collection of coupons contains exactly j distinct types. Thus, for instance, if one stops after having previously obtained six coupons whose successive types were 2, 4, 2, 5, 4, 3, then one would have earned a net return of 4r -6. The...
There were 3 different types of coupons that could be used in a grocery store 2...
There were 3 different types of coupons that could be used in a grocery store 2 weeks ago. The following table gives the frequency of the number of coupons used by a sample of people who came grocery shopping 2 weeks ago. Number of coupons Frequency 0 10 1 10 2 10 3 10 What is the midpoint of the first class? a)0.5 b)1 c) 0 d) 10
Problem 1. Stanislaw is collecting coupons. Each day he receives randomly one of n distinct coupons...
Problem 1. Stanislaw is collecting coupons. Each day he receives randomly one of n distinct coupons with equal probabilities (independently of other days (a) Let T be the number of days it takes Stanislaw to obtain a complete set. Explain why T can be written as a sum of n independent Geometric random variables and say what their parameters are (b) Compute the expected value of T. (Use the fact that the expectation of a sum of random variables is...
Sa of 10 > Suppose a biologist studying the mechanical limitations of growth among different species...
Sa of 10 > Suppose a biologist studying the mechanical limitations of growth among different species of tulips monitors a nation preserve. He collects data on the heights of 10 different types of tulips in the reserve and rounds cach height to the nea centimeter. 25, 21,26, 24, 27,30, 29,25, 16,23 Compute the first quartile (Q1). the third quartile (Os), and the interquartile range (IQR) of the data set. 021 cm 03 28 cm IQR 25 cm
Suppose that there are 12 types of coupons and that each time one obtains a coupon, it is, independently of previous selections, equally likely to be any one of the 12 types. One random variable of interest is T, the number of coupons that needs to be collected until one obtains a complete set of at least one of each type. Determine the p.m.f. of T, P(T -n) based on the fact P(T- n) P(T> n-1) P(T> n)
Suppose that...
4. Suppose you continually collect coupons and that there are two different types of coupon, type A and type B. Suppose also that each time a new coupon is obtained it is a type A coupon with probability 1/3 and a type B coupon with probability 2/3, independently of what coupons you have collected so far. Let X be the number of coupons collected until you have at least one coupon of both types. (a) Find the probability mass function...
1. Suppose there are m 2 1 different types of coupons, and a total of n coupons is to be collected. Each new coupon collected is, independent of the past, a type i coupon with probability i, 1 < i< m. Define for i-1,... ,m, Х,-{ 0, otherwise 1, if at least one type i coupon is among the n collected, type Let X = Xut + x,n. Calculate E(X) and Var(X).
Suppose there are n type of coupons. Each new coupon collected is of type i with probability Pi, independently of any other collected coupon. Here, D=1 Pi = 1. Suppose k coupons are collected. Let A be the event that there is at least one coupon of type i among the k collected. For i #j, (1) Compute P(A|AU A;) (2) Compute P(A|Aj)
Exercise 12.6 At each stage, one can either pay 1 and receive a coupon that is equally likely to be any of n types, or one can stop and receive a final reward of jr if one's current collection of coupons contains exactly j distinct types. Thus, for instance, if one stops after having previously obtained six coupons whose successive types were 2, 4, 2, 5, 4, 3, then one would have earned a net return of 4r -6. The...
Problem 1. Stanislaw is collecting coupons. Each day he receives randomly one of n distinct coupons with equal probabilities (independently of other days (a) Let T be the number of days it takes Stanislaw to obtain a complete set. Explain why T can be written as a sum of n independent Geometric random variables and say what their parameters are (b) Compute the expected value of T. (Use the fact that the expectation of a sum of random variables is...
Sa of 10 > Suppose a biologist studying the mechanical limitations of growth among different species of tulips monitors a nation preserve. He collects data on the heights of 10 different types of tulips in the reserve and rounds cach height to the nea centimeter. 25, 21,26, 24, 27,30, 29,25, 16,23 Compute the first quartile (Q1). the third quartile (Os), and the interquartile range (IQR) of the data set. 021 cm 03 28 cm IQR 25 cm
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