Discrete random variables — Question 285
Original QCE Vault practice · 5 marks
Q285 · Practice questionTechnology-freeSimple familiar5 marks
QUESTION 285 (5 marks)
The number X of bonus stamps in a pack has the distribution P(X=0)=k, P(X=1)=2k, P(X=2)=k and P(X=4)=2k. 
b)Determine E(X) and Var(X). c)Determine P(X≥E(X)). WORKED SOLUTION
Practice marking scheme
5 marksANSWERa) k=61. b) E(X)=2, Var(X)=37. c) 21. Worked solution
a) The probabilities sum to 6k=1. b) E(X)=(2+2+8)/6=2. Also E(X2)=(2+4+32)/6=19/3, so variance is 19/3−4=7/3. c) Since E(X)=2, P(X≥2)=k+2k=1/2. Exact answers unless rounding is specified; equivalent forms accepted.
b) Determines E(X squared).
b) Determines the variance.
c) Determines the requested probability.
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