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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A hand consists of 44 cards from a well-shuffled deck of 52 cards. a. Find the total number of possible 44-card poker hands. b. A blackblack flush is a 44-card hand consisting of all blackblack cards. Find the number of possible blackblack flushes. c. Find the probability of being dealt a blackblack flush.
2. Let {F.}n>o be the Fibonacci sequence. Find a homogeneous linear recurrence with constant coefficients that is satisfied by the sequence , = 2" + F.
Figure 1 shows a sample path of a Poisson process where the sequence of random variables, {S1, S2, ...}, show the arrival times and the sequence, {X1, X2, ...}, consists of the interarrival times that are i.i.d. exponential random variables with E[X;] = 1/A. %3D 3. Š, Š, S, S, Figure 1: A sample path of a Poisson process. nd A such that S = AX where X = [X1 X2 X3 X4]T and S = [S1 S2 S3 Sa]™. Find fs(s) using fx(x) and A (a) (b) Hint: You may take the determinant of A as 1. 2.
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?
Determine if the sequence {b„} is a solution to the recurrence relation an = 2an-1 + 3an-2, Vn > 2. %3D a) bn = 3n+1, Vn > 0 b) bn = n+1, Vn > 0 %3D %3D
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1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)– P(BnC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC) = 1– P(A^)P(B^)P(C*) = 1– (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 2/5, the probability that B hits it is 5/9, and the probability that C hits the target is 3/7. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p > 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1 — р)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0006 and n = 750, and then round your result to a…

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