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1) Neighborhood of downtown Baltimore, parking lot charges $7 per day. A car illegally parked on the street will be fined $25 if caught, with a 60% probability of getting caught. Should they park in lot or illegally?
- C= random variable = cost to park per day if done illegally.
- C can take values A= {25,0}
- P(f=25)= 0.60 [Prob. of getting caught 60%, price of $25]
- P(c=0)= 0.40 [Prob. of not getting caught 40%, price $0]
- E(c)= 25 P(c=25) + 0 P(c=0)
- = 25 (0.60) + 0 (0.40)
- = $15, eventually it will be worth it to park in the neighborhood instead of illegally.
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2) In a lottery, a player pays $1 and selects four distinct numbers from 0 to 9. Then, from an urn containing 10 identical balls numbered from 0 to 9, four balls are drawn at random
and without replacement. If the numbers of three or all four of these balls matches the player’s numbers, he wins $5 and $10, respectively. Otherwise, he loses. On the average,
how much money does the player gain per game? (Gain = win − loss.)
- G= Gain= Win-Loss
- Value G can take A= {10-1, 5-1, 0-1} = {9,4,-1}
E(G)= 9*P(G=9)+4(P=4)-P(G=-1)
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3) Mr. Jones is about to purchase a business. There are 2 businesses available. The first has a daily expectation profit of $150 and a std. dev. of $30. The 2nd had a daily profit of $150 and a std. dev. of $55. If Mr. Jones is interested in the most steady daily average profit, what business should he purchase?
Let's choose k=2, 2 std. devs.= 2σ (This should be in the question like "use 2 std. dev's)
1st business:
2nd business:
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4) Side length of random cubic die manufactured by a factory is a random number between 1 and 1.25 cm. What is probability that volume of randomly selected die is greater than 1.424 cm³?
- L is a random variable }
- L³ is also a random variable}
- These two are interested in
- P(L³>1.424=P(L>∛1.424)
= 0.4998
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5) In USA, probability of twins being born is . Let x=# of births at hospital till first twin is born. Calculate the percent a twin is born on the ith birth. Note a twin is born and a nontwin birth is .
Calculate P(x=i)
A= {T, NT, NNT, NNNT, NNNNT, ...}
The event A=i is associated with NNN...NT (This represents i-1. The NT is the ith birth)
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6) Someone claimed that is a main function and I have to check that it is.
For n= 0,1,2,..., insurance claims filed per week.
Check
We need to check
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