## Question

###### 1Define the probability density of the events Xi and Xz as:0.00 0.150.30 0.150.20 0.100.10 0.00(a) Calculate (i) Pr(X; > 2|X,=I) and (ii) Pr(Xz=I X, >2) . (b) Calculate Pr( X, Xz = 0) and (ii) Pr(X; + X, > 4) (c) A random sample of 2 is taken from the variable Xi write out the jointprobability distribution of these two random variables_ (d) Write out the probability distribution of the sample mean from the random sample of 2 obtained in (c)

1Define the probability density of the events Xi and Xz as: 0.00 0.15 0.30 0.15 0.20 0.10 0.10 0.00 (a) Calculate (i) Pr(X; > 2|X,=I) and (ii) Pr(Xz=I X, >2) . (b) Calculate Pr( X, Xz = 0) and (ii) Pr(X; + X, > 4) (c) A random sample of 2 is taken from the variable Xi write out the jointprobability distribution of these two random variables_ (d) Write out the probability distribution of the sample mean from the random sample of 2 obtained in (c)

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