A fair coin is tossed 3 times in a row. What is the probability that heads appears on only the last toss?
2 answers:
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Answer:
See explanation below.
Explanation:
Let X the random variable that represent the demand for the magazine, the pmf for X is given by:
X 1 2 3 4 5 6
P(X) 1/15 2/15 3/15 4/15 3/15 2/15
3 magazines
For this case the total spent is 2*3 = $ 6
And the net revenue for this case would be:
$4-$6 = -$2 , X=1 (demand 1)
$4*2-$6 = $2 , X=2 (demand 2)
$4*3-$6 = $6 , X=3 (demand 3)
For the values of X=4,5,6 the net revenue will be $6 since the number of magazines is 3
And the expected value for the net revenue would be:
4 magazines
For this case the total spent is 2*4 = $ 8
And the net revenue for this case would be:
$4-$8 = -$4 , X=1 (demand 1)
$4*2-$8 = $0 , X=2 (demand 2)
$4*3-$8 = $4 , X=3 (demand 3)
$4*4-$8 = $8 , X=4 (demand 4)
For the values of X=5,6 the net revenue will be $8 since the number of magazines is 4
And the expected value for the net revenue would be:
As as we can see we have a higher expected value for the case with 4 magazines.