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29.07.2020 •
Mathematics
Consider some 4-sided dice. Roll two of these dice. Let X be the minimum of the two values that appear. Let Y denote the maximum. Let Aj be the event containing all outcomes in which the minimum of the two dice is j or greater. Let Xi indicate whether Aj occurs.
Then X = X1 + X2 + X3 + X4.
a) Give the set of all outcomes when rolling the two 4-sided die.
b) Give the list of elements that are in each of Ai, A2, A3 and A4.
c) Find P(A for each j =1, 2, 3 and 4.e
d) Find the expected value of X by finding the expected value of the sum of the indicator variables.
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Ответ:
a) is TRUE
b) is FALSE
c) is TRUE
Step-by-step explanation:
Let's call the propositions
P: Laura is in the seventh grade
Q: Laura got an A on the mathematics test
R:Sarah got an A on the mathematics test
Then we have that the following propositions are true
P, Q v R (Q or R) and R---> ~P (if R then not P)
By watching at the truth table attached, we can see that the only row that satisfies all that conditions is the second one highlighted.
From there we can deduct that,
a) is TRUE
b) is FALSE
c) is TRUE