F(x,y) = { (x+y)/42 ; x = 1,2,3 y = 1,2 0; elsewhere ] (i) Find the mean for the random variable X. (ii) Find the mean for the random variable Y. (iii) Find the covariance Cov[X,Y]
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F(x,y) = { (x+y)/42 ; x = 1,2,3 y = 1,2
0; elsewhere ]
(i) Find the mean for the random variable X.
(ii) Find the mean for the random variable Y.
(iii) Find the
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- The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationLet X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure. 3₂ (0, 1) (-1,0) (a) Find Cov(Y₁ Y₂). Cov(Y₁, Y₂) = (b) Are Y₁ and Y₂ independent? Yes O No (1, 0) (c) Find the coefficient of correlation for Y₁ and Y₂. P= y/₁ (d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not? O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent. Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent. O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent. O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.
- Calculate correlation and probable error between physical parameters (temperature and humidity) Number of families(x)=2 Number of sites(n)= 1 Temperature(y) in autumn= 24.1 Humidity(y) in autumn= 35 20 1 19 Calculate correlation and probable error between physical parameters (temperature and humidity) Using the following formula coefficient of correlation (r). r = n([xy)-([x) (Ey) V[n(Ex 2)-(Ex) 2][n(Ey2)-([y) 2] ICov(X,Y) 1) The correlation of two random variables X and Y, usually written as p(X,Y)= Var (X)Var (Y) where Cov(...) is the covariance and Var(.) is the variance of random variables. Let X be a uniform random variable on the interval [0; 1], and let Y = X2. Find the correlation between X and Y.Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.
- 9. (25 points) Let X and Y be a random variables of the continuous type having the joint pdf f(x, y) = 8xy, %3D (a) [10 points] Find fa(1) and fy(y). (b) [15 points] Find Cov(X,Y) and correlation coefficient.Value of Y 14 22 30 40 65 0.02 0.05 0.10 0.03 0.01 Value of X 5 0.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 0.09Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.
- (1) Let X b(16,- 5,-) find E(4- 3x) and distribution function.f(x) = ² (2 − x) for -1 ≤ x ≤ c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X> 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is