1 Prove that a random q-ary code with rate R> 0 with high probability has relative distance8 > H7'(1 – 2R – E). Note that this is worse than the bound for random linear codes in|Hint : Your argument should show that the probability of having distance at leastdzH-1q(1-2R-e)ōzHq-1(1-2R-e) is 1-0(1)1-0(1), i.e. the probability should go to 1 as the blocklength n→o

Given:: Prove that a random q-ary code with rate R>0 with high probability has relative distance…

Answered: Prove that a random q-ary code with…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

See similar textbooks

Similar questions

Explain the differences between Gaussian elimination and Gauss-Jordan elimination.
Suppose we have the quadratic function f(x)=A(x^2)+2X+C where the random variables A and C have densities fA(x)=(x/2) for 0≤x≤2, and fC(x)=3(x^2) for 0≤x≤1. Assume A and C are independent. Find the probability that f(x) has real roo
Why the 1st row and 1st column of the JACOBIAN MATRX is always Zero ?
Q4) Given A = 1 -2 1 find the Kernel and 0 2 1 range of A.
show all solution 1. Suppose X is a random variable with E(X2)=10 and E(X)=2. Find the following: a) E(2X + 5) b) Var(X) c) Var(2X + 5) d) Var(2X – 5)
Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.
Students at certain university have to pass of one these three courses (MAT102, STA105, and PHY110). The pass rates for the courses MAT 102, STA105, and PHY110 are 0.54, 0.79, and 0.86, respectively. Suppose that 30 candidates take the MAT102 course, 25 take the STA105 course and 20 take the PHY110 coruse. A student takes one of these courses and passes. What are the probabilities that she took MAT102, STA105 or PHY110? Hint: Denote by Q the event a student to pass their course. Now denote by R1, R2 and R3 the events to take courses MAT102, STA105, and PHY110. The pass reates then represent the conditional probabilites: P(Q| R1), P(Q| R2) and P(Q| R3). The number of students taking the courses can be used to estimate the probabilities for R1, R2 and R3. For example, since there are total of 30 + 25 + 20 = 75 students that take the courses, for R1 we have: P(R1) = 30/75 = 2/5 What you are asked is: given that a student passes (event Q) estimate the probabilities that she took MAT102…
/islexe/1o_u-gNslkr7j8P3jH-IBXUFpICaple7CZVA31Oukg7ipxo7uCNytIJ nt) Ouestion Attempt: 1 of 1 Time Remaining: 4. 6 he values of x and z. X = (11x +21)- (8x- 12)
Q4) a) Let 6, and 0, be two unbiased estimators of 0. Show that ô, = aổ, +(1-a), 0sasl is an unbiased estimator of 0. Note that a convex combination of , and 0,. In addition, assume that and ô, are independent, and vo, ) = a; and vl@, )= a How should the constant a be chosen in order to minimize the variance of :? f(x,0)= {2 (1+ €x) -1sxs1 otherwise b) Consider the pdf i) Use the MOM to estimate 0. ii)Show that =3X is unbiased estimator for 0.
The following data shows the death cases of COVID-19, x and the number of positive COVID-19 cases, y in Malaysia from 29 December 2021 until 5 January 2022. Positive cases, y Death cases, X Date 29/12/2021 224 5 30/12/2021 241 1 31/12/2021 1/1/2022 205 191 6 2/1/2022 135 1 3/1/2022 167 4/1/2022 206 1 5/1/2022 245 2 e) Compute the value of the correlation coefficient and comment. f) Compute the value of coefficient determination and comment.
Suppose X~ Binom(6, p) and define an estimator T ==to estimate p. Then, variance 6. of T is, p(1–p) a) Var (T)= 6. b) Var (T) = 6 p(1 – p) c) Var (T)~ p(1-p) d) Var (T) - 36р

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS