Suppose X is a continuous random variable with distribution function f proportional to (x/ x^2+1)
for 0 ≤x≤10.
1. Identify the constant C so that f(x) =C(x/x^2+1).
2. Compute P(X >1|X <7).
for 0 ≤x≤10.
1. Identify the constant C so that f(x) =C(x/x^2+1).
2. Compute P(X >1|X <7).
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Alex
If you find the area under f using integration from 0 to 10 ....
∫ (x/x^2+1)dx = 2.30756
Since all probability density functions MUST integrate to 1, then ...
C = 1 / 2.30756 = 0.433358
2) For this problem, first integrate f(x) from 0 to 7 as this will give you ...
P(X < 7) = 0.84765353
Do the same from 1 to 7 ...
P(1 < X < 7) = 0.697463
P(X >1|X <7) = 0.697463 / 0.84765353 = 0.822816
hope that helped
If you find the area under f using integration from 0 to 10 ....
∫ (x/x^2+1)dx = 2.30756
Since all probability density functions MUST integrate to 1, then ...
C = 1 / 2.30756 = 0.433358
2) For this problem, first integrate f(x) from 0 to 7 as this will give you ...
P(X < 7) = 0.84765353
Do the same from 1 to 7 ...
P(1 < X < 7) = 0.697463
P(X >1|X <7) = 0.697463 / 0.84765353 = 0.822816
hope that helped