5. Consider three events: E1, E2, and F. Assume that P(F) > 0, and that P(E, N E2|F) = P(E,|F)P(E2|F). Is it necessarily always the case that P(E, N E2) = P(E1)P(E2)? Prove or find a counterexample.

Q: dp dq 2 if p = In(q7 + 7). Find dp dq ||

A: Simply use the chain rule of derivative and simplify.

Q: E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F).

A:

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A:

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Q: Probability. Don't understand.

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A: The provided information is as follows:The probability mass function of  is .

Q: Let B1, ... , Bn be independent events. Show n n P(ÜB.) = 1- T1c (1— Р(B,)). i=1 1=1

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Q: J and K are independent events. P(J | K) = 0.76. Find P(J) P(J) =

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Q: E, F are independent events. P(E) = 0.2, P(F) = 0.3. Find P(E ∪ F).

A: From the provided information, P (E) = 0.2 P (F) = 0.3 The events are independent.

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A:

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Q: J and K are independent events. P(J | K) = 0.6. Find P(J). %3D

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A:

Q: (d) If we define the events A and B by: A = {(X,Y):2(Y – X) > Y + X} Determine P(Ān B).

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