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Chapter 8: Q. 8.3 (page 392)

Compute the measurement signal-to-noise ratio that is, |μ|/σ, where μ = E[X] and σ2 = Var(X) of the

following random variables:

(a) Poisson with mean λ;

(b) binomial with parameters n and p;

(c) geometric with mean 1/p;

(d) uniform over (a, b);

(e) exponential with mean 1/λ;

(f) normal with parameters μ, σ2.

Short Answer

Expert verified

The values of N for each sub-parts are

a.)𝜆b.)np(1-p)c.)1qd.)3(a+b)(b-a)e.)1f.)𝜇𝜎

Step by step solution

01

Given information

Let N denote signal-to-noise ratio of random variable X.

N=𝜇𝜎

where,

E(X)=𝜇andVar(X)=𝜎2

02

Part (a)

For Poisson distribution we have,

N=𝜆𝜆=𝜆

03

Part (b)

For binomial distribution

N=npnp(1-p)=np1-p
04

Part (c)

For geometric distribution, we have

N=1pqp2=1q
05

Part (d)

For uniform distribution, we have

N=a+b/2b-a2/12=3(a+b)(b-a)
06

Part (e)

For exponential distribution, we have

N=1𝜆1/𝜆2=1
07

Part (f)

For normal distibution, we have

N=𝜇𝜎2=𝜇𝜎

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