1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...

Question

Question

1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...

1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥ a), where a > 0. Compare the upper bound with the actual value of P(X ≥ a).

b) Let X ∼ Exponential(λ). Using Chebyshev’s inequality find an upper bound for P(|X − EX| ≥ b), where b > 0.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

1) Here . The mean and variances are

a) The Markov's inequality is .

The upper bound is

.The actual value is

b)The Chebyshev's inequality is

The upper bound for is .

Add a comment

Answer 2

Similar Homework Help Questions

Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).

Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
5. Let X > 0 be a random variable with EX = 10 and EX2 =...

5. Let X > 0 be a random variable with EX = 10 and EX2 = 140. a. Find an upper bound on P(X > 14) involving EX using Markov's inequality. b. Modify the proof of Markov's inequality to find an upper bound on P(X > 14) in- volving EX? c. Compare the results in (a) and (b) above to what you find from Chebyshev's inequality.
Using Chebyshevs inequality, find an upper bound on: にsum.NG X, in にsum.NG X, in

Using Chebyshevs inequality, find an upper bound on: にsum.NG X, in にsum.NG X, in

Let X~Exponential(1). For P(X 2 4), evaluate: Markov's inequality, Chebyshev's inequality, . the exact value

Let X~Exponential(1). For P(X 2 4), evaluate: Markov's inequality, Chebyshev's inequality, . the exact value
Let X be Exponential variable with mean 1/λ. (a) Find E[X|X < c] using a calculation...

Let X be Exponential variable with mean 1/λ. (a) Find E[X|X < c] using a calculation from conditional density of X|X < c. [You can use the fact that: integral from 0 to c of Axe^(−Ax)dx = −ce^(−Ac) + 1/A (1 − e^(−Ac)).] (b) Find another way to calculate E[X|X < c] using the memoryless property
Please show your work with a brief but logical explanation. Suppose X is a random variable with p(X 0) 4/5, p(X-1) 1/10, p(X-9) 1/10. Then (a) Compute Var [X] and B [X] (b) What is the upper bound on...

Please show your work with a brief but logical explanation. Suppose X is a random variable with p(X 0) 4/5, p(X-1) 1/10, p(X-9) 1/10. Then (a) Compute Var [X] and B [X] (b) What is the upper bound on the probability that X is at least 20 obained by applying Markov's inequality? c) What is the upper bound on the probability that X is at least 20 obained by applying Chebychev's inequality'? Suppose X is a random variable with p(X...

5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x)...

5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x) dr-1. (b) Find F(x). Of course there is a separate answer for x 2 0 and x <0 (c Let X have an exponential density with parameter λ > 0 Prove the 'Inemoryless" property: P(X > t + s|X > s) = P(X > t) for t > 0 and s > 0. For example, the probability that the conversation lasts at least t...
Let X be uniform on [0, 1], and let Y be exponential with rate λ, so...

Let X be uniform on [0, 1], and let Y be exponential with rate λ, so that P(Y ≥ t) = e ^(−λt ) t ≥ 0 and 1 if t < 0 Assume that X and Y are independent, and define W = X + 2Y . a) For any w ≥ 0 and x ∈ [0, 1], compute P(W ≥ w|X = x) b) By undoing the conditioning on X, use the result from part (a) to compute...
Let X be an exponential random variable with parameter λ, so fX(x) = λe −λxu(x). Find...

Let X be an exponential random variable with parameter λ, so fX(x) = λe −λxu(x). Find the probability mass function of the the random variable Y = 1, if X < 1/λ Y = 0, if X >= 1/λ

Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2...

Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2 and E[X] = 2.5.

1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...

Homework Answers

Add Answer to:
1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...

Post as a guest

Earn Coins

Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).

5. Let X > 0 be a random variable with EX = 10 and EX2 =...

Using Chebyshevs inequality, find an upper bound on: にsum.NG X, in にsum.NG X, in

Let X~Exponential(1). For P(X 2 4), evaluate: Markov's inequality, Chebyshev's inequality, . the exact value

Let X be Exponential variable with mean 1/λ. (a) Find E[X|X < c] using a calculation...

Please show your work with a brief but logical explanation. Suppose X is a random variable with p(X 0) 4/5, p(X-1) 1/10, p(X-9) 1/10. Then (a) Compute Var [X] and B [X] (b) What is the upper bound on...

5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x)...

Let X be uniform on [0, 1], and let Y be exponential with rate λ, so...

Let X be an exponential random variable with parameter λ, so fX(x) = λe −λxu(x). Find...

Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2...

1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...

Homework Answers

Add Answer to: 1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...

Post as a guest

Earn Coins

Add Answer to:
1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥...