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1. The random varable x can only take three possibe values: wth prob-0.3, 2 with prob-0.3...
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variab...
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variables and k is a constant. (a) E(k) = k (b) E(X+Y) = E(X) + E(Y) (c) E(X/Y) + E(X)/E(Y) (d) E(X+Y) E(X)*E(Y) (unless what?) (e) E(X2) # (E(X)]? (1) E(kX) = E(X) 3. For random variable X with mean H. variance is defined var(X) = Ef(X-M.)'. Show how variance can be expressed only in terms of E(X) and E(X). 4....
Consider a discrete random variable X that can assume three values 1, 2, and k with...
Consider a discrete random variable X that can assume three values 1, 2, and k with respective probabilities 0.2, 0.5, and 0.3. If E(X) = 2.7, what is the value of k? Select one: a. 3 b. 1 c. 4 d. 5 e. 2
2. Explain in words, and words only, the following properties of expected values. NOTE: X and...
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variables and k is a constant. (a) E(k) = k (b) E(X+Y) = E(X) + E(Y) (c) E(X/Y) + E(X)/E(Y) (d) E(X+Y) E(X)*E(Y) (unless what?) (e) E(X2) # (E(X)]? (1) E(kX) = E(X) 3. For random variable X with mean H. variance is defined var(X) = Ef(X-M.)'. Show how variance can be expressed only in terms of E(X) and E(X). 4....
Let random variable X take the values 5, 5 and 12 with respective probabilities 0.2, 0.4...
Let random variable X take the values 5, 5 and 12 with respective probabilities 0.2, 0.4 and 0.4. a.What is the expected value of X? b.What is the variance of X? c.What is the standard deviation of X?
3% 1. Here are the probability distributions for three investment project returns: Up (prob = Down...
3% 1. Here are the probability distributions for three investment project returns: Up (prob = Down (prob = 0.4) 0.6) 5% -2% -2. 5% 14% -8% a. Without calculation, which two assets (X&Y, Y&Z, or X&Z) can reach the goal of diversification, which not? Explain. b. Calculate the expected return and standard deviation of each project and explain which one a rational investor would choose. c. Given your answer in part a., if you can only split your investment by...
Here are the probability distributions for three investment project returns: Up (prob = Down (prob =...
Here are the probability distributions for three investment project returns: Up (prob = Down (prob = 0.4) 0.6) -2% -2.5% 3% 14% -8% 5% Calculate the expected return and standard deviation of each project and explain which one a rational investor would choose. b)Given your answer in part a., if you can only split your investment by half, which two projects would you invest in, and what becomes the expected return and standard deviation of your portfolio?
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
X is a Discrete Random Variable that can take five values Given The five possible values...
X is a Discrete Random Variable that can take five values Given The five possible values are: x1 = 4 (Units not given) X2 = 6 (Units not given) X3 = 9 (Units not given) X4 = 12 (Units not given) X5 = 15 (Units not given) The associated probabilities are: p(x1) = 0.14 (Unitless) p(x2) = 0.11 (Unitless) p(x3) = 0.10 (Unitless) p(xx) = 0.25 (Unitless) Question(s) 1. If the five values are collectively exhaustive, what is p(x5)? (Unitless)...
2) Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X=1) =0.2, P(X=2) = 0.3, P(X=3) = 0.3, and P(X=4)= 0.1. A. Generate 400 values of this random variable with...
2) Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X=1) =0.2, P(X=2) = 0.3, P(X=3) = 0.3, and P(X=4)= 0.1. A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated...
A Suppose X and Y are random variables that only take on the values 0, 1,...
A Suppose X and Y are random variables that only take on the values 0, 1, and 2. (That is, for both of their probability mass functions, p(z) = 0 for xメ0.1.2.) Suppose E(X-Ely and E X2 EY]. Prove that EEY (Write your answer in complete sentences, as this requires a proof.)
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variables and k is a constant. (a) E(k) = k (b) E(X+Y) = E(X) + E(Y) (c) E(X/Y) + E(X)/E(Y) (d) E(X+Y) E(X)*E(Y) (unless what?) (e) E(X2) # (E(X)]? (1) E(kX) = E(X) 3. For random variable X with mean H. variance is defined var(X) = Ef(X-M.)'. Show how variance can be expressed only in terms of E(X) and E(X). 4....
2. Explain in words, and words only, the following properties of expected values. NOTE: X and Y are random variables and k is a constant. (a) E(k) = k (b) E(X+Y) = E(X) + E(Y) (c) E(X/Y) + E(X)/E(Y) (d) E(X+Y) E(X)*E(Y) (unless what?) (e) E(X2) # (E(X)]? (1) E(kX) = E(X) 3. For random variable X with mean H. variance is defined var(X) = Ef(X-M.)'. Show how variance can be expressed only in terms of E(X) and E(X). 4....
3% 1. Here are the probability distributions for three investment project returns: Up (prob = Down (prob = 0.4) 0.6) 5% -2% -2. 5% 14% -8% a. Without calculation, which two assets (X&Y, Y&Z, or X&Z) can reach the goal of diversification, which not? Explain. b. Calculate the expected return and standard deviation of each project and explain which one a rational investor would choose. c. Given your answer in part a., if you can only split your investment by...
Here are the probability distributions for three investment project returns: Up (prob = Down (prob = 0.4) 0.6) -2% -2.5% 3% 14% -8% 5% Calculate the expected return and standard deviation of each project and explain which one a rational investor would choose. b)Given your answer in part a., if you can only split your investment by half, which two projects would you invest in, and what becomes the expected return and standard deviation of your portfolio?
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
X is a Discrete Random Variable that can take five values Given The five possible values are: x1 = 4 (Units not given) X2 = 6 (Units not given) X3 = 9 (Units not given) X4 = 12 (Units not given) X5 = 15 (Units not given) The associated probabilities are: p(x1) = 0.14 (Unitless) p(x2) = 0.11 (Unitless) p(x3) = 0.10 (Unitless) p(xx) = 0.25 (Unitless) Question(s) 1. If the five values are collectively exhaustive, what is p(x5)? (Unitless)...
A Suppose X and Y are random variables that only take on the values 0, 1, and 2. (That is, for both of their probability mass functions, p(z) = 0 for xメ0.1.2.) Suppose E(X-Ely and E X2 EY]. Prove that EEY (Write your answer in complete sentences, as this requires a proof.)
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