A repeated appearance of the same symbol in a sequence is called a "run". For example the sequence 0111001 contains four runs: 0, 111, 00,and 1; the sequence 00010 contains three runs: 000, 1, and 0; and the sequence 111 contains a single run -- the sequence itself.Find the expected number of runs in the random sequence X,X2 where X1 and X2 are independent B2/3 (Bernoulli with parameter 2/3)random variables. For example, if X1 = 1 and X2= 0, the sequence is 10 and has 2 runs.Find the expected number of runs in the random sequence X1X2X3X4X5, where all X;'s are independent B2/3 random variables.

The given random sequence is independent with bernaulli parameter 2/3

Answered: repeated appearance of the ame symbol…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2- Consider a binary 3-bit communication system that transmits either zeros or ones with with probability pi and p2 respectively. Transmitting probabilities have a ratio of p1 /p2 = 3/4. Because of channel noise, a transmitted zero is received as a one with probability a , with a similar random corruption a transmitted one is received as a zero by error. Note that all possible 3-bit sequences (2 = 8 different ones such that “000"...to... “111") can be received at remote site due to random noise, regardless of whatever host sent or vice versa. a) Compute the probability of receiving “101" in terms of a . Consider, transmitted sequence could be any one of them above. b) Suppose a sequence “101" is received, what is the probability that "101" was actually transmitted, in terms of a ?
Fill in the gaps with one or more words: A.B,M and X are random variables. If A and B are independant then they _____ uncorrelated. If E(MX)= E(M)E(X) then M and X _____ independant.
Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
In a certain industry, roughly 40% of managers have an advanced degree (Master's or beyond). From a group of 10 managers, X represents the number of them who have an advanced degree. What model is most appropriate for X? A. Poisson B. Binomial C. Binomial with n=10 and p=0.40 D.Poisson with λ = 4
People are classified as hypertensive if their systolic bloodpressure (SBP) is higher than a specified level for their agegroup, according to the algorithm in Table 5.1.Assume SBP is normally distributed with mean andstandard deviation given in Table 5.1 for age groups 1−14and 15−44, respectively. Define a family as a group of twopeople in age group 1−14 and two people in age group15−44. A family is classified as hypertensive if at least oneadult and at least one child are hypertensive. 5.17) What proportion of 1- to 14-year-olds are hypertensive? 5.18) What proportion of 15- to 44-year-olds are hyper-tensive?
Digital communications 2
On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 19 trials of this experiment: 171, 212, 285, 175, 202, 269, 193, 217, 164, 231, 261, 236, 186, 257, 271, 229, 250, 296, 226 Send data to calculator Find 20th and 75th percentiles for these reaction times. (If necessary, consult a list of formulas.) (a) The 20th percentile: milliseconds (b) The 75th percentile: milliseconds
13-7. What is the expected number of heads appearing when a fair coin is tossed three 3-28) es Co times
If telephone calls arrive at a computer telephone service on the average of 30 calls hour in accordance with a Poisson process, what is the probability that per the computer operator will have to wait less than 9.39 minutes for the next nine calls to arrive?

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