For each probability experiment, determine the number of outcomes and identify the sample space . 1. A probability experiment consists of recording a response to the survey statement at the left and the gender of the respondent. 2. A probability experiment consists of recording a response to the survey statement at the left and the age (18–34, 35–49, 50 and older) of the respondent. 3. A probability experiment consists of recording a response to the survey statement at the left and the geographic location (Northeast, South, Midwest, West) of the respondent. Answer: Page A33
For each probability experiment, determine the number of outcomes and identify the sample space . 1. A probability experiment consists of recording a response to the survey statement at the left and the gender of the respondent. 2. A probability experiment consists of recording a response to the survey statement at the left and the age (18–34, 35–49, 50 and older) of the respondent. 3. A probability experiment consists of recording a response to the survey statement at the left and the geographic location (Northeast, South, Midwest, West) of the respondent. Answer: Page A33
For each probability experiment, determine the number of outcomes and identify the sample space.
1. A probability experiment consists of recording a response to the survey statement at the left and the gender of the respondent.
2. A probability experiment consists of recording a response to the survey statement at the left and the age (18–34, 35–49, 50 and older) of the respondent.
3. A probability experiment consists of recording a response to the survey statement at the left and the geographic location (Northeast, South, Midwest, West) of the respondent.
Answer: Page A33
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
8 (Correlation and Diversification)
Assume we have two stocks, A and B, show that a particular combination
of the two stocks produce a risk-free portfolio when the correlation between
the return of A and B is -1.
9 (Portfolio allocation)
Suppose R₁ and R2 are returns of 2 assets and with expected return and
variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find
−∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest
risk.
7 (Multivariate random variable)
Suppose X, €1, €2, €3 are IID N(0, 1) and
Y2
Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3.
=
(In models like this, X is called the common factors of Y₁, Y₂, Y3.)
Y = (Y1, Y2, Y3).
(a) Find E(Y) and cov(Y).
(b) What can you observe from cov(Y).
Write
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