The simultaneous probability distribution of the random variables X and Y is given below. - 2 - 1 Y 0 0.25 0.10 0.00 0.10 0.10 0.10 1 0.00 0.10 0.25 a) Find the marginal distribution for X. b) Find...


The simultaneous probability distribution of the random variables X and Y is given below.<br>- 2<br>- 1<br>Y 0<br>0.25<br>0.10<br>0.00<br>0.10<br>0.10<br>0.10<br>1<br>0.00<br>0.10<br>0.25<br>a) Find the marginal distribution for X.<br>b) Find the expected value and standard deviation for X.<br>c) Find the marginal distribution for Y.<br>d) Find the expected value and standard deviation for Y.<br>e) Are the random variables X and Y independent?<br>f) Find the covariance between X and Y.<br>g) Find the correlation between X and Y.<br>h) Find the expected value and standard deviation for W = 0.5X + 3Y.<br>

Extracted text: The simultaneous probability distribution of the random variables X and Y is given below. - 2 - 1 Y 0 0.25 0.10 0.00 0.10 0.10 0.10 1 0.00 0.10 0.25 a) Find the marginal distribution for X. b) Find the expected value and standard deviation for X. c) Find the marginal distribution for Y. d) Find the expected value and standard deviation for Y. e) Are the random variables X and Y independent? f) Find the covariance between X and Y. g) Find the correlation between X and Y. h) Find the expected value and standard deviation for W = 0.5X + 3Y.

Jun 08, 2022
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