PROBLEM 1. [5 points] Value-at-Risk (VaR). The random variable Y measures the change in market value...

Question

Question

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

PROBLEM 1. [5 points] Value-at-Risk (VaR). The random variable Y measures the change in market va...

PROBLEM 1. [5 points] Value-at-Risk (VaR). The random variable Y measures the change in market value of a portfolio during a given time period. The variable Y is assumed to be normal with N(μ,02). (a) Calculate the VaR (Value-at-Risk) with confidence level 1-α, 0 < α < 1, (b) In particular, calculate VaR with confidence level 75% if Y N(0.2, 0.32) PROBLEM 1. [5 points] Value-at-Risk (VaR). The random variable Y measures the change in market value of a portfolio...
1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y)...

1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y) 1600. It is known that P(Y>80| X = 50) 0.1 and P(Y 22 X 40) 0.7886 (1) What is the correlation coefficient between X and Y? (2) What is the expected value of Y given X 50?
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....

value at risk at level p, p is between 0 and 1 Q2. Denote by Ф...

value at risk at level p, p is between 0 and 1 Q2. Denote by Ф the standard normal distribution (that is, with mean zero and variance 1), and by ф_l the corresponding quantile function. Let X be a normal random variable with mean μ and variance σ2. Evaluate VaRx (p) in terms of ф-1, , 1 and σ. Hint: X = ơZ + μ, where Z is standard normal
value at risk at level p, p is between 0 to 1 Q2. Denote by Ф...

value at risk at level p, p is between 0 to 1 Q2. Denote by Ф the standard normal distribution (that is, with mean zero and variance 1), and by ф_l the corresponding quantile function. Let X be a normal random variable with mean μ and variance σ2. Evaluate VaRx (p) in terms of ф-1, , 1 and σ. Hint: X = ơZ + μ, where Z is standard normal
Suppose that X is a standard normal random variable with mean 0 and variance 1 and...

Suppose that X is a standard normal random variable with mean 0 and variance 1 and that we know how to generate X. Explain how you would generate Y from a normal density with mean μ and variance σ"? That is, given that we already generated a random variate X from N(0,1), how would you convert X into Y so that Y follows N (μ, σ 2)?

. Suppose that Y is a normal random variable with mean µ = 3 and variance...

. Suppose that Y is a normal random variable with mean µ = 3 and variance σ 2 = 1; i.e., Y dist = N(3, 1). Also suppose that X is a binomial random variable with n = 2 and p = 1/4; i.e., X dist = Bin(2, 1/4). Suppose X and Y are independent random variables. Find the expected value of Y X. Hint: Consider conditioning on the events {X = j} for j = 0, 1, 2. 8....
problems binomial random, veriable has the moment generating function, y(t)=E eux 1. A nd+ 1-p)n. Show...

problems binomial random, veriable has the moment generating function, y(t)=E eux 1. A nd+ 1-p)n. Show that EIX|-np and Var(X) np(1-p) using that EIX)-v(0) nd E.X2 =ψ (0). 2. Lex X be uniformly distributed over (a b). Show that ElXI 쌓 and Var(X) = (b and second moments of this random variable where the pdf of X is (x)N of a continuous randonn variable is defined as E[X"-广.nf(z)dz. )a using the first Note that the nth moment 3. Show that...
Problem 1. (a) Let X be a Binomial random variable such that E(X) 4 and Var(x)...

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.

Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2...

Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2 and X is another normally distributed random variable with μ-: 5 and σ-5. Y and X are independent. Calculate the following probabilities according to a normal distribution table (e.g., a normal table found from the Internet) (1) (4 points) Pr(Y> 12) (2) (4 points) Pr(2 < X <4) (3) (4 points) Pr(Y> 12 and 2< X <4) and Pr(Y> 12 or 2< X <4)...