The moment generating function (mgf) of y is given by
![M_y(t)=E(e^{ty})=E(e^{2pxt})=M_x(2pt)=p(1-e^{2pt}(1-p))^{-1}](https://tex.z-dn.net/?f=M_y%28t%29%3DE%28e%5E%7Bty%7D%29%3DE%28e%5E%7B2pxt%7D%29%3DM_x%282pt%29%3Dp%281-e%5E%7B2pt%7D%281-p%29%29%5E%7B-1%7D)
Since the momoent generating function of x is given by
![M_x(t)=p(1-e^{t}(1-p))^{-1}](https://tex.z-dn.net/?f=M_x%28t%29%3Dp%281-e%5E%7Bt%7D%281-p%29%29%5E%7B-1%7D)
When p tends to 0, we have
![\lim_{p \to 0} M_y(t)= \lim_{p \to 0} \frac{p}{1-e^{2pt}(1-p)} = \frac{0}{0}](https://tex.z-dn.net/?f=%20%5Clim_%7Bp%20%5Cto%200%7D%20M_y%28t%29%3D%20%20%5Clim_%7Bp%20%5Cto%200%7D%20%20%5Cfrac%7Bp%7D%7B1-e%5E%7B2pt%7D%281-p%29%7D%20%3D%20%5Cfrac%7B0%7D%7B0%7D%20)
Applying L'Hopital's rule we have:
![\lim_{p \to 0} M_y(t)=\lim_{p \to 0} \frac{1}{e^{2pt}+2te^{2pt}+2pte^{2pt}} = \frac{1}{1+2t} , \ \ \ t\ \textless \ \frac{1}{2}](https://tex.z-dn.net/?f=%5Clim_%7Bp%20%5Cto%200%7D%20M_y%28t%29%3D%5Clim_%7Bp%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7Be%5E%7B2pt%7D%2B2te%5E%7B2pt%7D%2B2pte%5E%7B2pt%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B1%2B2t%7D%20%2C%20%5C%20%5C%20%5C%20t%5C%20%5Ctextless%20%5C%20%20%5Cfrac%7B1%7D%7B2%7D%20)
This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.
Answer:
3x +2
Step-by-step explanation:
3x-7+9
Combine like terms
3x +2
It is indeed the rearranging of neuritis to the ground.
65 percent thats your answer when you convert the number easy as that<span />