query: How to show that if $X \sim \Gamma(n/2, 1/2)$ and $Y \sim \Gamma(1/2, 1/2)$ then $X + Y \sim \Gamma((n+1)/2, 1/2)$?
positive_passages.docid: 24889
positive_passages.text: Sum of independent Gamma distributions is a Gamma distribution
negative_passages.docid: 67454
negative_passages.text: Show that $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^n (x_i - \bar{x})(y_i)$.
negative_passages.docid: 126962
negative_passages.text: Differentiation under integral sign (Gamma function)
negative_passages.docid: 129605
negative_passages.text: $ 2g(z)=g(\frac{z}{2}) + g(\frac{z+1}{2})$
negative_passages.docid: 28332
negative_passages.text: Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$
negative_passages.docid: 109223
negative_passages.text: For ordinals $\delta$ and $\beta$, if $\delta\in$ or $=\beta$, then there exists $\gamma\in$ or $=\beta$ such that $\beta=\delta+\gamma$
negative_passages.docid: 100907
negative_passages.text: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 96036
negative_passages.text: If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc?
negative_passages.docid: 106753
negative_passages.text: Conditional expection of gamma distribution on sum
negative_passages.docid: 23603
negative_passages.text: Joint distribution of $X+Y$ and $\frac{X}{X+Y}$
negative_passages.docid: 7775
negative_passages.text: Show that $|x-y|\leq |x|+|y|$.
negative_passages.docid: 83531
negative_passages.text: Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
negative_passages.docid: 1305
negative_passages.text: Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
negative_passages.docid: 10968
negative_passages.text: Let $X \sim Bin(n,p)$ show that $X/n \nsim Bin()$
negative_passages.docid: 133870
negative_passages.text: if $\alpha\leq\beta$ then there is $\gamma$ such as $\alpha+\gamma=\beta$
negative_passages.docid: 82742
negative_passages.text: Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $