A cascade system has the following characteristics for its three stages:

Stage $1$: Gain G$1=10$ dB $,$ Noise figure F$1=3dB.$

Stage $2$: Gain G$2=15$ dB $,$ Noise figure F$2=5dB.$

Stage $3$: Gain G$3=20$ dB $,$ Noise figure F$3=4dB.$

Calculate:

$($a$)$ Calculate the total noise figure of the cascade system.

$($b$)$ If the system is at room temperature $)=(290K,$ find the equivalent noise temperature of the system.