Problem 2, using Chebyshev's inequality, estimate the probability that a random variable X ~ Г (4...
chebyshev’s inequality Problem 2 Chebyshev's Inequality Suppose that the random variable ? has a Poisson distribution with the parameter ? > 0, ~ ?(A). Using the Chebyshev's inequality prove that Problem 3 - Application of the Chebyshev's Inequality Suppose that a player plays a game where he gains a dollar with the probability or loses a dollar with the probability . That is, his gain from one game can be modeled as a random variable fi, such that If the...
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....
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...
4. Compare the Chebyshev inequality and the exact probability for the event X ->c as a function of c for the following cases. (a) X is a uniform random variable in the intervall-b, b (b) X is a binomial random variable with n-10, p-05. 4. Compare the Chebyshev inequality and the exact probability for the event X ->c as a function of c for the following cases. (a) X is a uniform random variable in the intervall-b, b (b) X...
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.
A random variable X has a mean μ = 10 and a variance σ2-4. Using Chebyshev's theorem, find (a) P(X-101-3); (b) P(X-101 < 3); (c) P(5<X<15) (d) the value of the constant c such that P(X 100.04
Let X~Exponential(1). For P(X 2 4), evaluate: Markov's inequality, Chebyshev's inequality, . the exact value
Problem 4 (20p). Let α > 0, and for each n E N let Xn : Ω → R be a random variable on a probability space (Q,F,P) with the gamma distribution「an. Does there exist a random variable X:82 → R such that Xn-,X as n →oo? Problem 4 (20p). Let α > 0, and for each n E N let Xn : Ω → R be a random variable on a probability space (Q,F,P) with the gamma distribution「an. Does...
Use Chebyshev's Inequality to get a lower bound for the number of times a fair coin must be tossed in order for the probability to be at least 0.90 that the ratio of the observed number of heads to the total number of tosses be between 0.4 and 0.6. Let X be a random variable with μ=10 and σ=4. A sample of size 100 is taken from this population. Find the probability that the sum of these 100 observations is less...
e a continuous random variable with E(X)-11 and try to estimate μ using these two estinators from a random sample X1, . . . , Xn: For what a and b are both estimators unbiased and the relative efficiency of to μ2 is 45n?