query: Let $X$ and $Y$ be independent random variables of exponential distribution with mean $1$. Find the mean of $Z=\min \{X,Y\}$.
positive_passages.docid: 77938
positive_passages.text: How to prove that minimum of two exponential random variables is another exponential random variable?
negative_passages.docid: 70221
negative_passages.text: Probability about three independent exponential random variables
negative_passages.docid: 72813
negative_passages.text: If $X$ and $Y$ are uniformly distributed on $(0,1)$, what is the distribution of $\max(X,Y)/\min(X,Y)$?
negative_passages.docid: 40243
negative_passages.text: Pdf of the difference of two exponentially distributed random variables
negative_passages.docid: 64493
negative_passages.text: $X$ is a Geometric random variable find the expectation of $1/X$
negative_passages.docid: 116975
negative_passages.text: Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
negative_passages.docid: 69392
negative_passages.text: How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
negative_passages.docid: 115355
negative_passages.text: Find $E(\max(X,Y))$ for $X$, $Y$ independent standard normal
negative_passages.docid: 67738
negative_passages.text: Mean Value theorem problem?(inequality)
negative_passages.docid: 85079
negative_passages.text: Calculating the expected values of the min/max of 2 random variables
negative_passages.docid: 134508
negative_passages.text: Distribution of Ratio of Exponential and Gamma random variable
negative_passages.docid: 117907
negative_passages.text: A question regarding independence of $\min{\{X,Y\}}$ and $X-Y$ when $X,Y$ follows iid geometric distribution
negative_passages.docid: 152495
negative_passages.text: Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
negative_passages.docid: 155114
negative_passages.text: Find the marginal pdf of $X$ and $Y$
negative_passages.docid: 122929
negative_passages.text: Prove that $Y=-2\sum_{i=1}^n \ln F_{X_i}(X_i)$ have distribution $\chi^2(2n)$
negative_passages.docid: 48332
negative_passages.text: Why does the minimum value of $x^x$ equal $1/e$?
negative_passages.docid: 42861
negative_passages.text: Inverse of sum of exponential random variables (mean and variance)