Q:

The density function of a random variable X is given by: f(x)={(cx , 0<X<2 0 otherwise)┤ Find the value of c

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The density function of a random variable X is given by:
f(x)={(cx               ,   0<X<2 0                        otherwise)┤
Find the value of c.

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 Since        ∫_(-∞)^∞ 〖f(x)〗 dx=1
∴1=c∫_0^2 x dx=c/2 [x^2 ]_0^2=2c→c=1/2

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