Sonya and Isaac are in motorboats located at the center of a lake. At time t=0, Sonya begins traveling south at a speed of 36 mp
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a) Add up all the probabilities where
:
b) The expected value is
Since X is the number of absent students on Monday, the expectation E[X] is the number of students you can expect to be absent on average on any given Monday. According to the distribution, you can expect around 3 students to be consistently absent.
c) The variance is
where
So the variance is
The standard deviation is the square root of the variance:
d) Since is a linear combination of
, computing the expectation and variance of Y is easy:
e) The covariance of X and Y is
We have
so
Then the covariance is
f) Dividing the covariance by the variance of X gives