Paragraph Styles a fair die is tossed. If the mmber of spote showingis ether 4 a
ID: 3062979 • Letter: P
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Paragraph Styles a fair die is tossed. If the mmber of spote showingis ether 4 ar 5 you win $2, if the mumber of spots showing is 6 you win $8, and if the number of spots showing is 1, 2, or 3 you win nothing. Let Xbe the amount that you win. The expected value of Xis A)$0.00. B)$1.00 C)$2.00. D) $4.00 E) Noae of the above 4. toss a penny and observe whether it lands heads up or tails up. Suppose the penany is fair, i e, the probability of heads is 1/2 and the probability of tails is 1/2. This means A Every occurrence of a head must be balanced by a tail in one of the next two or three tosses B. IfI flip the coin many, many times, the proportion of heads will be approximately 1/2 and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases C. Regardless of the number of flips, half will be heads and half tails D. All of the above. 5. Event A occurs with probability 0.3 and event B occurs with probability 04. If A and B are independent, we may conclude A) PA and B)-0.12 C) PCBA) = 0.4. D) all of the above Anormal density curve has which of the following properties? A) It is symmetic B) It has a peak centered above its mean C) The spread of the curve is proportional to the standard deviation D) All of the above. 6. Event .d occurs with probability 0.2. Event B occurs with probabilty 0 8 lfd and B are dspont (mutually exclusive) then A) 84 and B) = 0.16. PlA and B)-1.0 or B) = 0.16. C) D)Explanation / Answer
5. P(A)=0.3
P(B)=0.4
A and B are independent => P( A and B )=P(A).P(B)=0.12
P(A|B) = P(A and B)/P(B) = P(A).P(B)/P(B) = P(A) = 0.3
Similarly, P(B|A) = P(B) = 0.4
Hence, all above are correct. Option (D)
6. Normal density curve is symmetric since for normal distribution, f(x) = f(-x), for all x
Normal density curve is peak centered above it's mean since Mode of normal distribution is the mean if the normal distribution.
By definition of standard deviation, option (C) is also correct.
Hence, all of the above is correct. Option (D)
7. P(A)=0.2
P(B)=0.8
A and B are disjoint => P(A and B) = 0.
P(A or B) = P(A) + P(B) - P(A and B) = 1 Option (B)
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