Question

PDF of a random variable X is given as :

$f_X\left(x\right)=\lambda exp(-\lambda x);x\ge 0;\lambda >0$.

If mean of X is 1/a and variance is 1/b, then which graph shows the correct relationship between 'a' and 'b'.

• A.
• B.
• C.
• D. None

Answer 1

The correct option is B

$E\left[X\right]={\int }_0^{n}x{f}_x\left(x\right)dx=\frac{1}{\lambda }=\frac{1}{a}\Rightarrow a=\lambda$

$Var\left[X^2\right]=\frac{1}{{\lambda }^2}=\frac{1}{b}\Rightarrow b={\lambda }^2$

$\Rightarrow b=a^2$