DRV $X$ is equally likely to take the values $0^\circ\, , 45^\circ \, , 90^\circ$. Determine the expected value of $\sin X$.
My attempt:
I tried $\sum_{x=0}^3 \frac{\sin x}{3}$ but the answer is wrong…
[Math] Determine the expected value of $\sin X$.
expectationprobabilityrandom variables
Best Answer
Expected value is calculated as $$E(X)=\sum_{i=1}^nX_ip_i$$ You have a random variable $X$ which can take values $0,45,90$ equally likely so the probability for each is $1/3$. You want expected values of $\sin X$, since $X$ takes 3 values calculate $\sin X$ at these values and multiply by the probability. $$E(\sin X)=\frac13(\sin0+\sin 45+\sin90)$$