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If events X and Y are independent, what must be true? Check all that apply.
P(
YX) = 0
P(
XY)=0
P(YX) = P(Y)
PY|X) = P(X)
OPXY)=P(Y)
P(X|Y) = P(X)

Respuesta :

Answer:

P(Y | X)= P(Y)

P(X | Y)= P(X)

Step-by-step explanation:

If events X and Y are independent, then following results are true:

  • [tex]P(Y/X) = P(Y)[/tex]
  • [tex]P(X/Y) = P(X)[/tex]

What are independent events?

" Independent events are defined as the events which are not depend on any other events."

Condition used for independent events

[tex]P(X\cap Y) = P(X) \times P(Y)[/tex]

According to the question,

Given event X and Y are independent,

[tex]P(X/Y) = \frac{P(X\cap Y)}{P(Y)}[/tex]

Substitute the value of [tex]P(X\cap Y)[/tex] we get,

[tex]P(X/Y) = \frac{P(X) \times P(Y)}{P(Y)}[/tex]

             [tex]= P(X)[/tex]

Similarly for independent events X and Y we have,

[tex]P(Y/X) = \frac{P(X\cap Y)}{P(X)}[/tex]

Substitute the value of [tex]P(X\cap Y)[/tex] we get,

[tex]P(Y/X) = \frac{P(X) \times P(Y)}{P(X)}[/tex]

             [tex]= P(Y)[/tex]

Hence, if events X and Y are independent, then following results are true:

  • [tex]P(Y/X) = P(Y)[/tex]
  • [tex]P(X/Y) = P(X)[/tex]

Learn more about independent events here

brainly.com/question/13488890

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