The partial products are: 42 x 28 = (40 + 2) x (20 + 8) = 40 x 20 + 40 x 8 + 2 x 20 + 2 x 8
= 800 + 320 + 40 + 16 Hope this helped.
Answer:
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Answer:
(3C1 × 4C1)/12C2
Step-by-step explanation:
Total electives = 3 + 4 + 5 = 12
Art: 3C1
History: 4C1
1 Art & 1 History = 3C1 × 4C1
Probability = (3C1 × 4C1)/12C2
Answer:
tex]M=\beta ln(2)[/tex]
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate).
Solution to the problem
For this case we can use the following Theorem:
"If X is a continuos random variable of the exponential distribution with parameter
for some
"
Then the median of X is 
Proof
Let M the median for the random variable X.
From the definition for the exponential distribution we know the denisty function of X is given by:

Since we need the median we can put this equation:

If we evaluate the integral we got this:
![\frac{1}{\beta} \int_0^M e^{- \frac{x}{\beta}}dx =\frac{1}{\beta} [-\beta e^{-\frac{x}{\beta}}] \Big|_0^M](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cbeta%7D%20%5Cint_0%5EM%20e%5E%7B-%20%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7Ddx%20%3D%5Cfrac%7B1%7D%7B%5Cbeta%7D%20%5B-%5Cbeta%20e%5E%7B-%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7D%5D%20%5CBig%7C_0%5EM)
And that's equal to:

And if we solve for M we got:


If we apply natural log on both sides we got:

And then 