Question

kes a math wizard to conjure a magic square is a random ing an exponential distribution with an expected value of 8. Assuming that each variable hav conjuring is independent, what is the probability that the wizard will take less than 14 minutes to conjure two magic squares?

Answer 1

For one magic square, expected value = 8

So,

for 2 magic squares, expected value is given by:

$\frac{1}{\lambda }=8\times 2=16$

So,

$\lambda =\frac{1}{16}$

Probability Density Function of t is given by:

$f(t)=\frac{1}{16}e^{-\frac{t}{16}}$

So,

$P(t<14)=\int_{0}^{14}f(t)dt=\int_{0}^{14}\frac{1}{16}e^{-\frac{t}{16}}dt$

$-e^{-\frac{t}{16}}$

between the limits 0 to 14.

Applying limts, we get:

$P(t<14)=-e^{-\frac{7}{8}}-(-1)=-0.4169&plus;1=0.5831$

So,

Answer is:

0.5831