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 Type i light bulbs function for a random amount of time having mean mui and standard deviation sigmai, i=1,2

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 Type i light bulbs function for a random amount of time having mean mui and standard deviation sigmai, i=1,2. A light bulb randomly chosen from a bin of bulbs is a type 1 bulb with probability p, and type 2 with prob. (1-p).
what is the expected value and the variance of the lifetime of this bulb?

2) Mx(t)=exp{2(e^t)-2) and My(t)=((3/4)(e^t)+(1/4))^10 X and Y are independent.
how do I find P{X+Y=2}, P{XY=0} and E(XY)?