Exponential Distribution

Q. $\text{Let}{X}_1\text{and}{X}_2$ be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then $Y=min(X_1,X_2)$ is

1. exponentially distributed with mean 1/6
2. exponentially distributed with mean 2
3. normally distributed with mean 3/4
4. normally distributed with mean 1/6

Q.

Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by
$F_z\left(x\right)=(\begin{array}{cc}1-e^{-x}& \mathrm{if}x\ge 0\\ 0& \mathrm{if}x<0\end{array}$
Then Pr(Z > 2 | Z > 1), rounded off to two decimal places, is equal to .

1. 0.367

Q. The number of parameters in the univariate exponential and Gaussian distributions, respectively are

1. 2 and 2
2. 1 and 2
3. 2 and 1
4. 1 and 1