Question

a. Assume E[X] is finite for a non-negative continuous random variable X. Prove that 1 −...

a. Assume E[X] is finite for a non-negative continuous random variable X. Prove that 1 − Fx (a) ≤ E[X]/a .
b. Assume the MX(t) exists for a continuous random variable X. Prove that 1−Fx(a)≤ Mx(t)/eta

Homework Answers

Answer #1

TOPIC:Markov's inequality.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Calculate the probability that X ≤ E[X] assuming that: (a) X is a continuous random variable...
Calculate the probability that X ≤ E[X] assuming that: (a) X is a continuous random variable with uniform distribution; (b) X is a continuous random variable with an Exp(1) distribution; (c) X is a discrete random variable with a Poisson(1) distribution. (d) X is continuous random variable with standard normal distribution.
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all...
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all t Find the probability mass function of X. (ii) Let X and Y be two independent continuous random variables with moment generating functions MX(t)=1/sqrt(1-t) and MY(t)=1/(1-t)^3/2, t<1 Calculate E(X+Y)^2
A continuous random variable may assume a. a finite number of values. b. only one value...
A continuous random variable may assume a. a finite number of values. b. only one value c. all values in an interval or collection of intervals d. all positive integers e. Non-numerical values such as categories or types 1 points    QUESTION 9 Let F be the cumulative distribution function for a continuous random variable X. It is known at the following 5 points. F(0)=0 F(1)=0.4 F(2)=0.7 F(3)=0.9 F(4)=1 Which of the following is wrong? a. Pr(1<X<3)=50% b. Pr(X<0)=100% c....
The moment generating function for the random variable X is MX(t) = (e^t/ (1−t )) if...
The moment generating function for the random variable X is MX(t) = (e^t/ (1−t )) if |t| < 1. Find the variance of X.
Prove that if X and Y are non-negative independent random variables, then X^2 is independent of...
Prove that if X and Y are non-negative independent random variables, then X^2 is independent of Y^2. *** Please prove using independent random variables or variance or linearity of variance, or binomial variance.
Suppose that X is a continuous random variable with a probability density function that is a...
Suppose that X is a continuous random variable with a probability density function that is a positive constant on the interval [8,20], and is 0 otherwise. a. What is the positive constant mentioned above? b. Calculate P(10?X?15). c. Find an expression for the CDF FX(x). Calculate the following values. FX(7)= FX(11)= FX(30)=
Let X be a continuous random variable with a probability density function fX (x) = 2xI...
Let X be a continuous random variable with a probability density function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) = e^−x a. Find the expression for the probability density function fY (y). b. Find the domain of the probability density function fY (y).
3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0...
3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0 < x < 1. (a) Find the value of c such that fX(x) is indeed a PDF. Is this PDF bounded? (b) Determine and sketch the graph of the CDF of X. (c) Compute each of the following: (i) P(X > 0.5). (ii) P(X = 0). (ii) The median of X. (ii) The mean of X.
Let X be a continuous random variable with the following probability density function: f(x) = e^−(x−1)...
Let X be a continuous random variable with the following probability density function: f(x) = e^−(x−1) for x ≥ 1; 0 elsewhere (i) Find P(0.5 < X < 2). (ii) Find the value such that random variable X exceeds it 50% of the time. This value is called the median of the random variable X.
real analysis (a) prove that e^x is continuous at x=0 (b) using (a) prove that it...
real analysis (a) prove that e^x is continuous at x=0 (b) using (a) prove that it is continuous for all x (c) prove that lnx is continuous for positive x
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT