Interactive practice questions
For a random variable, consider the probability density function $f\left(x\right)=\frac{x^2}{9}$f(x)=x29 over $0\le x\le3$0≤x≤3 and $f\left(x\right)=0$f(x)=0 elsewhere.
State the cumulative distribution function $F\left(x\right)$F(x) over $0\le x\le3$0≤x≤3 where $F\left(x\right)=0$F(x)=0 for $x<0$x<0 and $F\left(x\right)=1$F(x)=1 for $x>3$x>3.
Use $C$C as the constant of integration.
For a random variable, consider the probability density function $f\left(x\right)=\frac{e^x}{e^4-1}$f(x)=exe4−1 over $0\le x\le4$0≤x≤4 and $f\left(x\right)=0$f(x)=0 elsewhere.
For a random variable, consider the probability density function $f\left(x\right)=\frac{3x\left(8-x\right)}{135}$f(x)=3x(8−x)135 over $\left[2,5\right]$[2,5] and $f\left(x\right)=0$f(x)=0 elsewhere.
For a random variable, consider the following probability density function.