Problem 1 Let X be a RV with expected value E{X} = 0 and variance Var{x}...
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....
Find the expected value E(X), the variance Var(X) and the standard deviation σ(X) for the density function. (Round your answers to four decimal places.) f(x) = 1 x on [1, e] E(X) = Var(X) = σ(X) =
1 0.7 Find the Expected value and the variance of X. E (X)=EXP(X) Var(x)-o? And -E(x?)-me a) Note: = px E(X2)-DFP(%) b) Consider the following information for a binomial N- number of trials or experiments-5 distribution: x-number of success -3 Probability of uccess-sp- 04 and probability of filur 1p-0.6 Find the probability of 3 successes out of 5 trials: Note P(x): Nex px (1-p)NX Note: Nex NI / x! (Naji
Find the expected value E(X), the variance Var(X) and the standard deviation σ(X) for each of the density functions in f (x) = 3 4 (1 − x2) on [−1, 1]
Problem 4: Let X be a continuous variable with mean inequality find A 0 so that and variance ơ2. Using Chebyshev
1. Let X be an RV with density f(x) = ¼arosinx + c, x E [-1,11 (f(x) = 0 elsewhere). (a) Compute the constant c. (b) Compute the DF of X. (c) Compute the DF of the RV Y d) Compute P( <0.5) X2.
1. Let X be an RV with density f(x) = ¼arosinx + c, x E [-1,11 (f(x) = 0 elsewhere). (a) Compute the constant c. (b) Compute the DF of X. (c) Compute the DF of...
Let p0 =P(X=1) and suppose that 0<p0 <1. Let μ=E(X) and σ2 =var(X). a.) Find E[X|X ̸= 1] b.) Find var(X|X ̸= 1)
Problem 4 Suppose X1, ..., Xn ~ f(x) independently. Let u = E(Xi) and o2 = Var(Xi). Let X Xi/n. (1) Calculate E(X) and Var(X) (2) Explain that X -> u as n -> co. What is the shape of the density of X? (3) Let XiBernoulli(p), calculate u and a2 in terms of p. (4) Continue from (3), explain that X is the frequency of heads. Calculate E(X) and Var(X). Explain that X -> p. What is the shape...
Problem 1. (a) Let X be a Binomial random variable such that E(X) 4 and Var(x) 2. Find the parameters of X (b) Let X be a standard normal random variable. Write down one function f(t) so that the random variable Y-f(X) is normal with mean a and variance b.
How to slove it
Question 5. Let X and Y be random variables having expected value 0 and correlation p. Show that E Var(Y|X)| < (1 -β)Var(Y).