Answer the following questions about joint random variables. (a) When considering the correlation coefficient, does it measure a linear, quadratic, or cubic relationship between the variables? (b) When considering the correlation coefficient, how can you tell if there is a positive relationship, negative relationship, or no relationship between the variables? (c) Suppose we find that the joint probability distribution of X and Y to be x + 2y f(x, y) for x = 0, 1, 2; y= 1,2,3, 4. 72 you were to find the marginal distribution of Y, what would be the sum of the probabilities for the random variable Y be, and why? If

Please calculate the covariance and the correlation coefficient for the two random variables and briefly comment on the resulting correlation between the variables.

QUESTION 12 A random variable X has the following distribution: X -1 0 1 P(X=x) 3 .5 .2 Let Y=X². Find the expected value of random variable Y. .38 .6 0.5 4

QUESTION 12 A random variable X has the following distribution: X -1 0 1 P(X=x) 3 .5 .2 Let Y=X². Find the expected value of random variable Y. .38 .6 0.5 4

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 15 0 24 28 15 17 36 −9 −16 −16 y: 21 −8 27 10 10 27 22 −2 −3 −1

Can someone please help me with these questions.

Question 4: According to historic data, on average, 5 traffic accidents occur per month at intersection A. If the probability that more than 2 accidents happen at that intersection is more than a given threshold p, the municipality will take corrective actions to improve the intersection safety. You have been asked to investigate if the municipality should take corrective actions or not. What type of probability distribution should you use to check this and is this a discrete or continuous probability distribution? (a) Normal, Continuous (c) Binomial, Discrete (b) Poisson, Discrete (d) Exponential, Continuous Question 5: Which of the following distributions does not have a symmetric form? (a) Z~N(0,1) (c) t-distribution (b) Uniform distribution (d) x² distribution

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