The probability mass function of X will be a mixture of two geometric probability mass functions. If the first coupon is Type A
If the first coupon is Type B
So,
For expectation we first draw the first coupon and after that we calculate the expectation based on that.
4. Suppose you continually collect coupons and that there are two different types of coupon, type...
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)
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 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)
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...
Suppose that two teams, A and B play a series of games that ends when one of them has won 3 games. Suppose that games are played independently and both teams have equal chances of winning in each game. Let X be the number of games played. (i) Find the probability mass function of X. (ii) Find the expected value of X
A certain system can experience three different types of defects. Let A (i 1,2,3) denote the event that the system has a defect of type i. Suppose that PLAI) = 0.33. P(A2) = 0.37. P(43) = 0.37, P(A1 UA2) 0.58, P(A1 U A3) 0.63 (a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type...
A certain system can experience three different types of defects. Let A (i 1,2,3) denote the event that the system has a defect of type i. Suppose that PLAI) = 0.33. P(A2) = 0.37. P(43) = 0.37, P(A1 UA2) 0.58, P(A1 U A3) 0.63 (a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type...
4. Core i5 and i7 are two different types of CPU manufactured by Intel. As you may know as a matter of fact, Intel does not produce two types of CPUs. Instead, they just produce Core i7 chips. However, since a chip contains many millions of transistors, some of the transistors may not work properly, while other regions from the chip are working perfectly. In this case, Intel does not scrap the chip to trash, as it will be a...
2. A certain system can experience three different types of defects. Let A denote the event that the system has a defect of type i. Suppose that 1,2, 3 What is the probability that the system has a type 2 defect but not a type 3 defect? What is the probability that the system has at least one of these defects? What is the probability that the system has none of these defects?