(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X is exponentially distributed with mean s.

Find P(Sin(X)> 1/2)

2. Relevant equations

f_{X}(x) = se^{-sx}, x[tex]\geq[/tex] 0

0, otherwise

F_{X}(x) = 1 - e^{-sx}, x[tex]\geq[/tex] 0

0 otherwise

3. The attempt at a solution

Let Y = sin X

F_{Y}(y) = P(Y[tex]\leq[/tex] y)

= P(sinX [tex]\leq[/tex] Y)

= P(X [tex]\leq[/tex] arcsin(y), X[tex]\geq[/tex] [tex]\pi[/tex] - arcsin(y)){This is where I become slightly unsure}

=F_{X}(arcsin(y)) - F_{X}([tex]\pi[/tex] - arcsin(y))

=1-e^{-s(arcsin(y))}- (1-e^{-s([tex]\pi[/tex] - arcsin(y))})

From here I can differentiate to find the pdf and then use that to find sinX < 1/2.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Non 1-1 transformation of continuous random variable

**Physics Forums | Science Articles, Homework Help, Discussion**