Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( ) ?? + 0.4, 0 ≤ ? ≤ 2 0, ??ℎ?????? a. Find the value C that makes fX(x) a valid PDF. (Hint: Draw the PDF to start.) b. Find and sketch the CDF, FX(x). c. Calculate P[X > 1] d. Let A be the event that X > 1. Find and sketch the conditional PDF fX|A(x|A).
solving we get
C = 0.1
b)
cdf = P(X < x) =
c)
P(X > 1) = 1- P(X < 1)
= 1- 0.45
= 0.55
d)
P(X| X> 1) = (0.4 + 0.1x)/ 0.55
Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( )...
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