veudeje
2021-11-19
The table below contains the information for the joint probability mass function of X and Y (two different measurement systems).
a) Plot and calculate the marginal distributions of X and Y
b) Select one of the Y values from the table and find the conditional probability mass function of X for that Y value you have selected and plot it.
c) Show whether X and Y are independent or not.
d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).
Liek1993
Beginner2021-11-20Added 13 answers
Step 1
Given,
The table below contains the information for the joint probability mass function of X and Y (two different measurement systems).
Step 2
a) Plot and calculate the marginal distributions of X and Y.
The marginal distribution of X:
The marginal distribution of Y:
Step 3
b) To determine X's conditional probability given a value of
The conditional distribution is plotted:
Step 4
c) Show whether X and Y are independent or not.
If the variable X and Y are independent that satisfies,
or
Let take
Hence X and Y are not independent random variables
Step 5
d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).
Where,
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