csat-suneung 2012 Q28

csat-suneung · South-Korea · csat__math-humanities 4 marks Continuous Probability Distributions and Random Variables Change of Variable and Integral Evaluation
A continuous random variable $X$ defined on the interval $[ 0,1 ]$ has probability density function $f ( x )$. The mean of $X$ is $\frac { 1 } { 4 }$ and $\int _ { 0 } ^ { 1 } ( a x + 5 ) f ( x ) d x = 10$. Find the value of the constant $a$. [4 points] 
A continuous random variable $X$ defined on the interval $[ 0,1 ]$ has probability density function $f ( x )$. The mean of $X$ is $\frac { 1 } { 4 }$ and $\int _ { 0 } ^ { 1 } ( a x + 5 ) f ( x ) d x = 10$. Find the value of the constant $a$. [4 points]
Paper Questions
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