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Roll a pair of fair dice to get 2 numbers X1, X2. Flip a coin with p.pdf

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Roll a pair of fair dice to get 2 numbers X1, X2. Flip a coin with p=P(head)=0.2 to get another random variable Y, where Y=1 for head and Y=0 for tail. Let X= X1+X2-Y. A. Find the pmf and cdf of X. B. Calculate EX and E(2x-3) C. Find Var(X) and Var(3x+3) Solution I am not sure of this answer. p(0)=a P(1)=a p(2)=a/2 since sum of p(i)\'s add up to 1, a+a+a/2=1 5a/2=1 a=2/5 x=0,1,2 p(0)=2/5 p(1)=2/5 p(2)=1/5 CDF P(x <=0) = F(0) = 2/5 P(x <= 1)= F(1) = 4/5 P(x <=2)= F(2) =1.

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Roll a pair of fair dice to get 2 numbers X1, X2. Flip a coin with p=P(head)=0.2 to get another random variable Y, where Y=1 for head and Y=0 for tail. Let X= X1+X2-Y. A. Find the pmf and cdf of X. B. Calculate EX and E(2x-3) C. Find Var(X) and Var(3x+3) Solution I am not sure of this answer. p(0)=a P(1)=a p(2)=a/2 since sum of p(i)'s add up to 1, a+a+a/2=1 5a/2=1 a=2/5 x=0,1,2 p(0)=2/5 p(1)=2/5 p(2)=1/5 CDF P(x <=0) = F(0) = 2/5 P(x <= 1)= F(1) = 4/5 P(x <=2)= F(2) =1

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