Discrete random variables — Question 362
Original QCE Vault practice · 5 marks
Q362 · Practice questionTechnology-freeSimple familiar5 marks
QUESTION 362 (5 marks)
A fair four-sided die gives X∈{1,2,3,4}, each with probability 1/4. A game pays Y=4X−7 dollars. a)Determine the mean and variance of X. b)Determine the mean and variance of the payout Y. WORKED SOLUTION
Practice marking scheme
5 marksANSWERa) E(X)=5/2, Var(X)=5/4. b) E(Y)=3, Var(Y)=20. Worked solution
a) E(X)=10/4=5/2 and E(X2)=30/4=15/2. Subtract the squared mean. b) The equally likely values of Y are −3,1,5,9. Their mean is 3, and E(Y2)=(9+1+25+81)/4=29, giving variance 29−9=20. Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Lists the transformed outcomes or obtains the mean by an equivalent valid method.
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