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

Question

Question

Let X~Exponential(1). For P(X 2 4), evaluate: Markovs inequality, Chebyshevs inequality, . the exact value

math Statistics-And-Probability

Answer 1

Answer #1

C1) .e E(x)- 1 and V(X)1 FC2) (X): 1 and q=4 4- K2 K2

Answer 2

Similar Homework Help Questions

7. (a) State Chebyshev's inequality and prove it using Markov's inequality. 151 (b) Let (2, P)...

7. (a) State Chebyshev's inequality and prove it using Markov's inequality. 151 (b) Let (2, P) be a probability space representing a random experiment that can be repeated many times under the same conditions, and let A S2 be a random event. Suppose the experiment is repeated n times. (i) Write down an expression for the relative frequency of event A 131 ) Show that the relative frequence of A converges in probability to P(A) as the number of repetitions...
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.
3. Suppose that Z is standard normal. (a) In Chebyshev's inequality P(IZ 22) p, what is p*? (b) W...

3. Suppose that Z is standard normal. (a) In Chebyshev's inequality P(IZ 22) p, what is p*? (b) What is the actual value of P(IZ1 2 2)? 4. Suppose that X1, X2, .. . , X100 are iid with common (exponential) pdf f(x) = else. 0 (a) Give E S100 b) Give var S100 3. Suppose that Z is standard normal. (a) In Chebyshev's inequality P(IZ 22) p, what is p*? (b) What is the actual value of P(IZ1 2...

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).
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y)...

1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
2. Suppose that is an exponential random variable with pdf f(y)= e), y>0. a. Use Chebyshev's Inequality to get an up...

2. Suppose that is an exponential random variable with pdf f(y)= e), y>0. a. Use Chebyshev's Inequality to get an upper bound for the probability that takes on a value more than two standard deviations away from the mean. b. Use the given pdf to compute the exact probability that takes on a value more than two standard deviations away from the mean.

1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be ...

1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be (a) Find the cdf of X. (b) Find the mean and variance of X. 2. Suppose X is a Gamma random variable with pdf 「(a)go Show that the moment generating function is M(t) 3, Let X equal the nurnber out of n 48 mature aster seeds that will germinate when p- 0.75 is the probability that a particular seed germinates. Approximate...
Problem 2, using Chebyshev's inequality, estimate the probability that a random variable X ~ Г (4...

Problem 2, using Chebyshev's inequality, estimate the probability that a random variable X ~ Г (4, 10) satisfies |X - 0.42 0.2 Problem 3. For i.id. X1 , . . . , Xn ~ Exp(2), n = 200estimate from above Problem 2, using Chebyshev's inequality, estimate the probability that a random variable X ~ Г (4, 10) satisfies |X - 0.42 0.2 Problem 3. For i.id. X1 , . . . , Xn ~ Exp(2), n = 200estimate from above
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.

2 5. Suppose X is a discrete random variable that has a geometric distribution with p=...

2 5. Suppose X is a discrete random variable that has a geometric distribution with p= a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X > 6). [5] c. Use Chebyshev's Inequality to estimate P(X > 6). [5]