please help me with this problem in the probability. i find it very difficult so i need help

5. Suppose a lightbulb has a lifetime X that is exponentially distributed with mean 300 hours. (a) What is the probability the bulb lasts longer than 400 hours? (b) What is the standard deviation for the lifetime of the bulb? (c) What is the median of the lightbulb's distribution? (d) Given that the bulb has lasted over 260 hours, what is the probability it will last over 420 hours? (e) Suppose the bulb will be replaced once the bulb goes out or once the bulb's lifetime has reached 500 hours (whichever happens rst). Let Y be the time of the bulb's replacement. What is E (Y)? (f) Refer to (e). Suppose for each hour the bulb is on, it costs $25. Addi tionally, it costs $10 to install the bulb. Again let Y be the time of the bulb's replacement. What is the expected cost to maintain the rst bulb? (g) Refer to (e). What is E ()? (h) What is Var (X100)