The data for the joint probability mass function of X and Y (two different measurement systems) are given in the table below. a) Calculate the marginal distributions of X and Y and plot them. 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. f(x,y)1234150.100.10.05200.050.0500.12500.050.050.1300.10.050.150.05 d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).

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The data for the joint probability mass function of X and Y (two different measurement systems) are given in the table below.  a) Calculate the marginal distributions of X and Y and plot them.  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.  f(x,y)1234150.100.10.05200.050.0500.12500.050.050.1300.10.050.150.05  d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).

Alrew1959 · Accepted Answer

Step 1 Given: f(x,y)1234Total150.100.10.050.25200.050.0500.10.22500.050.050.10.2300.10.050.150.050.35total0.250.150.30.31 Step 2 a) Marginal distribution of X: XP(X)150.25200.2250.2300.35total1  XP(Y)10.2520.1530.340.3total1  Step 3 b) Let Y=2 P(X∣Y=2)=P(X,Y=2)P(Y=2) Probability distribution of X∣Y=2 XP(X|Y=2)150200.333333250.333333300.333333total1 Step 4 c) For X and Y to be independent, product of marginal probabilities should be equal to joint probability for all values of X and Y P(x=15)=0.25 P(Y=1)=0.25 P(x=15,y=1)=01 Here, 0.25⋅0.25=0.0625 (which is not equal to 0.1) Thus , X and Y are not independent of each other.

The data for the joint probability mass function of X and Y (two different measu

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