Question

15.1The probability density function of the X and Y compound random variables is given below.

X                                        Y

1

2

3

1

234

225

84

2

180

453

161

3

39

192

157

Accordingly, after finding the possibilities for each value, the expected value, variance and standard deviation; Interpret the asymmetry measure (a₃) when the 3rd moment (µ3 = 0.0005) according to the arithmetic mean and the kurtosis measure (a₄) when the 4th moment (µ4 = 0.004) according to the arithmetic mean. Then, find the covariance (Cov (X, Y)) and the Pearson correlation coefficient (r_xy) to determine whether the variables x and y are independent.

15.2 The necessity of X and Y continuous random variables works continuously.

fx=cx2y1+y                   0 ≤x≤3 ve 0 ≤y≤30                                        in other cases

Accordingly, after finding the possibilities for each value, the expected value, variance and standard deviation; Interpret the asymmetry measure (a₃) when the 3rd moment (µ3 = 0.0005) according to the arithmetic mean and the kurtosis measure (a₄) when the 4th moment (µ4 = 0.004) according to the arithmetic mean. Then, find the covariance (Cov (X, Y)) and the Pearson correlation coefficient (r_xy) to determine whether the variables x and y are independent.

Answer 1

*** Note , your question both 1 and 2 are incorrect because the question 2 does not proof to be an pdf ,,,,!!!!!.. just clear about your question, and properly upload it.