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Problem #10: The standard deviation of X, denoted by SD(X), is defined by SD(X) = V...
Suppose X is a normal with zero mean and standard deviation of $10 million. a) Find the value at risk for X for the risk tolerances h=0.01, 0.02, 0.05, 0.10, 0.50, 0.60, and 0.95. b) Is there a relation between VaR for values of h <= 0.50 and values for h>= 0.50?
A discrete random variable X is defined by the following probability distribution X 2 7 9 10 P ( X = x ) 0.08 0.12 0.38 0.42 Find the following : μ = E ( X ) E(X^2) . E ( 2X + 3 ) E ( 4X − 8 ) σ ^2 = Var ( X ) σ = SD ( X )
. Let X and Y be random variables. The conditional
variance of Y given X, denoted Var(Y | X),
is defined as
Var(Y | X) = E[Y
2
| X] − E[Y | X]
2
.
Show that Var(Y ) = E[Var(Y | X)] + Var(E[Y | X]). (This equality
you are showing is known
as the Law of Total Variance). Hint: From the Law of Total
Expectation, you get Var(Y ) =
E[Y
2
] − E[Y ]
2...
7. In each part of this problem a set of n vectors denoted V, , denoted V. Carefully follow these directions V, is given in a vector space i) Determine whether or not the n vectors are linearly independent. i) Determine whether or not the n vectors are a spanning set of V Then find a basis and the dimension of the subspace of V which is spanned by these n vectors. (This subspace may be V itself.) a. V...
Problem #7: suppose that vectors in R3 are denoted by 1 x 3 matrices and define T: R3 R3 by 3 7([xi x2 x3]) = [x1 x2 x3]| 4 3 0 0] 8 Find a basis for the range of T. Problem #7: Select
Problem 5-5 Suppose your expectations regarding the stock market are as follows: Probability State of the Economy Boom Normal growth Recession HPR 40% 20 E(A) = PODMG Var() = 02 - PD[C) – EMPA SD() = 0 = Var (7) Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not found intermediate calculation 1 of 5 ili Next > ere to search hin E() = Š P60576) Var(t) = 02 - P()[76) –...
7. Let V = {(x,y)|x,YER}. Suppose addition and scalar multiplication are defined using the following non-standard rules. [5 marks] (x,y,)+(x2,y2) = (y2 + y2,X, + x) c(x,,y.) = (cx ,2cy) where c is any real number. a. Find the result of (1, -2) + (4, -3) under the above operations.
can someone show the steps on
how to complete this problem thanks
22. Suppose that for a normal random variable X, ECx) what is sd(X), the standard deviation of the sample mean? - 10 and Var(X)-5.24. For a sample of size n 250, (a) 0.1448 (b) 0.2448 (c) 0.3448 (d) 0.4448 (e) 0.5448
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]
Please help Stats
2. The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution: 2 f(x) 2 0.11 5 7 8 10 0.27 0.16 0.14 0.32 (c) Suppose g(X) = (3X – 1)2. Find E[9(X)] (a) Find E(X). (b) Find E(X). 3. Use the distribution from Problem 2. (a) Find the variance of X, V(X). (b) Find the standard deviation of X, SD(X). (c) Find V(-3X). (d) Explain why V(X)...