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If-f-x-0-othrrwise-2x-0-x-a-is-a-probability-density-funtion-of-a-random-variable-then-a-pls-solve-




Question Number 180734 by srikanth2684 last updated on 16/Nov/22
If f(x)={_(0, othrrwise) ^(2x , 0≤x≤a)  is a probability  density funtion of a random   variable, then a=?  pls solve
$${If}\:{f}\left({x}\right)=\left\{_{\mathrm{0},\:{othrrwise}} ^{\mathrm{2}{x}\:,\:\mathrm{0}\leqslant{x}\leqslant{a}} \:{is}\:{a}\:{probability}\right. \\ $$$${density}\:{funtion}\:{of}\:{a}\:{random}\: \\ $$$${variable},\:{then}\:{a}=? \\ $$$${pls}\:{solve} \\ $$
Answered by cortano1 last updated on 16/Nov/22
 ∫_0 ^a  f(x)dx = 1⇒∫_0 ^a 2x dx=1  ⇒a^2  = 1; a=1 ( since a>0 )
$$\:\underset{\mathrm{0}} {\overset{{a}} {\int}}\:{f}\left({x}\right){dx}\:=\:\mathrm{1}\Rightarrow\underset{\mathrm{0}} {\overset{{a}} {\int}}\mathrm{2}{x}\:{dx}=\mathrm{1} \\ $$$$\Rightarrow{a}^{\mathrm{2}} \:=\:\mathrm{1};\:{a}=\mathrm{1}\:\left(\:\mathrm{since}\:{a}>\mathrm{0}\:\right) \\ $$
Commented by srikanth2684 last updated on 16/Nov/22
thank you
$${thank}\:{you} \\ $$

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