Well the first and last I'm having some troubles with, and 2-4 I think the logic I am using is correct but would like his verified since no answers were provided(adsbygoogle = window.adsbygoogle || []).push({});

What is [itex]P(A \cup B)[/itex] if [itex] P(A) = 0.2, P(A \cap B) = 0.1, P(B) = 0.5?[/itex]

Would that just be the prob. of being in A or B minus prob of being in both (prob of being in A + prob being in B - A int B). Would it depend on whether they are mutually exclusive or not? (how can we tell if thats all tahts given in the question).

I am kind of half between (A + B) and half between (A + B - AintB). But since A int B was included in the question, would that imply that I should use A + B - A int B = 0.2 + 0.5 - 0.1 = 0.6

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What is E(X) if Mx(u) = [itex](1-u)^{-3}, u<1[/itex]

To find E(X) find the first derivative:

= -3(1-u)^(-4).-1

= 3(1-u)^(-4)

and then let u -> 0

3(1)^(-4)

=3

Therefor E(X) = 3

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What is E([itex]X^{3}[/itex]) if fx(x) = 2x, 0<x<1

E(X^(3)) = integral (0,1) of 2x.x^3 dx

= int (0,1) 2x^4 dx

= 2/5 x^5 .. (0,1)

= 2/5

Therefor E(X^3)) = 2/5

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What is c if

g(x) = c|x|, x = -2, -1, 1, 2 is a probability function

For it to be a prob. function, the sum of all the probabilities must equal 1

2c + c + c + 2c = 1

c = 1/6

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What is [itex] P(\overline{B})[/itex] if [itex] P(B|\overline{A}) = 0.5, P(\overline{A}) = 0.3[/itex] [itex] and P(B|A) = 0.8 ?[/itex]

Well I'm a bit stuck on this question;

I used some multiplicative laws to find

[itex]P(A \cap B) = 0.56[/itex]

and [itex] P(B \cap \overline{A}) = 0.15 [/itex]

I'm not sure how to continue from here.

Thanks

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# Few set and prob questions

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