Need help with probability density functions

[quartz trench]

I don't really know how to do this because I'm not well acquainted with probability density functions

[scarlet gulch]

First, recall the definition of CDF:
F(x) = P(X < x)
So:
P(a ≤ X ≤ b) = P(X ≤ b) - P(X < a) = F(b+) - F(a)
P(X ≥ a) = 1 - P(X < a) = 1 - F(a)
Then, recall how to find the CDF if you know the PDF:
F(x) = ∫(f(t)dt, -∞, x)
So, now try expressing P(a ≤ X ≤ b) and P(X ≥ a) using the integral definition.

[quartz trench]

Does this makes sense?

[scarlet gulch]

Yeah, looks good.
Considering that X is most likely supposed to be absolutely continuous, we have P(a ≤ X ≤ b) = P(a ≤ X < b), so no need to calculate limits.

[quartz trench]

ty

[sharp glade]

@quartz trench has given 1 rep to @scarlet gulch