Sum of two uniform distributions and other questions.

*Assume that *

*X has uniform distribution on the interval [0,1] and Y **has uniform*

*distribution on the interval [0,**2]. Find the density of Z = X + Y .*

Would this just be 1+1/2 = 3/2?

*Suppose X with values (0, 1) has density $\displaystyle \[f(x) = cx^2(1-x)^2\]$ for 0 < x < 1. Find:*

*a) the constant c; b) E[X]; c) Var[X]*

I get, a) c = 30; b) 1/2; c) 1/28

*Transistors produced by one machine have a lifetime which is exponentially distributed with mean 100 hours. Those produced by a second machine have an exponentially distributed lifetime with mean 200 hours. A package of 12 transistors contains 4 produced by the first machine, and 8 produced by the second machine. Let X be the lifetime of a transistor picked at random from this package. Find:*

*a) P(X greater or equal to 200 hours); b) E[X]; c) Var[X]*

So would E[X] = (1/3)(100) + (2/3)(200) = 500/3? If so, then for a) I get e^(-6/5) = 0.3012, and for c) I get (500/3)^2 = 250000/9