Assume n and m are two integers such that n > m > 1. If a bit string of length n+m is randomly selected, what is the probability of selecting a string starting with m 0s?
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Assume n and m are two integers such that n > m > 1. If a bit string of length n+m is randomly selected, what is
the probability of selecting a string starting with m 0s?
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- How many ways can you select 4 numbers between 0 and 19 so that no two are consecutive? Hint: Can you rephrase this as a question about binary strings?Consider a binary code with 4 bits (0 or 1) in each code word. In each code word, abit is a zero with probability 0.6, independent of any other bit.(a) What is the probability of the code word 0101?(b) What is the probability that a code word contains exactly two ones?The ten digits are written on ten seperate cards - A card 95 chosen randomly, the digit neplaced. How many cards should be chosen to have at most on is noted and the card 93 one number greater than 5 among them with probability greater than 0-85.
- sketch a 5-input, 3-output switching element. time is slotted and synchronized for inputs. One slot holds at most one packet. A packet arrival processes to each input are Bernoulli (with arrival probability p for a packet in each slot and non arrival probability 1-p in each slot) (a) write an expression for the probability of one or more arrivals in a slot. (b) find the throughput at the output (c) write an expression for the probability in a slot that the top 3 inputs have packets and the bottom 2 doesn't have a packet. (d) for what values of p is the probability of 2 arrivals at the input greater than the probability of ine arrival at the inputs?(a) How many bit strings of length nine either begin with two 0s or end with three 1s?(b) How many different four-letter initials with none of the letters repeated can people have?(c) How many permutations of the letters WXYZABCD contain the strings ZAB and WD?(d) How many different strings can be made from the letters in HAMHANDEDNESSES, usingall the letters?You have 2n numbers such where each number i is repeated twice (1 ≤ i ≤ n). Given arandom permutation of these 2n numbers what is the expected number of adjacent pairs that havethe same value.For example, if n = 5, then the permutation 1 2 2 3 4 5 5 4 3 1 has two adjacent pairs that have thesame value.
- The Infinite Monkey Theorem states that a monkey hitting keys completely at random on a typewriter for an infinite amount of time will, eventually, type any given text. Even the complete works of William Shakespeare. Some quotes are truly amazing. Consider the famous quote by Gen George S. Patton: "WHEN IN DOUBT, ATTACK" That's 21 amazing characters. Suppose a monkey is seated in front of a KEYBOARD WITH 28 CHARACTERS (one for each of the 26 letters in the alphabet, plus the space bar, and a comma). Suppose the monkey types only 21 characters completely at random. If X is the number of different 21 character strings it could have typed, then the chances that it typed the quote is one divided by X. What is X? Group of answer choices 2.45651e+30 1.05230e+37 3.13330e+27 5.18132e+29Data were collected from a random sample of 330 home sales from a community in 2003. Let Price denote the selling price (in $1,000), BDR denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet), Lsize denote the lot size (in square feet), Age denote the age of the house (in years), and Poor denote a binary variable that is equal to 1 if the condition of the house is reported as "poor." An estimated regression yields Price=129.9 +0.529BDR+25.5Bath +0.170Hsize +0.004Lsize +0.098Age-53.2Poor, R² = 0.78, SER=45.2. Suppose that a homeowner converts part of an existing family room in her house into a new bathroom. What is the expected increase in the value of the house? The expected increase in the value of the house is $. (Round your response to the nearest dollar.) Suppose that a homeowner adds a new bathroom to her house, which increases the size of the house by 109 square feet. What is the expected increase in the value of…Find the number of ways to select 12 objects with repetition from 5 distinct types of objects with at least 1 objects of each type and at most 4 objects of each type.
