A stick of length l is broken at a uniformly chosen random location. We denote the length of the smaller piece by X. (a) Find th
1 answer:
Answer:
a)
b)
Step-by-step explanation:
a) Lets denote the cumulative distribution function of X. Note that for any value a between 0 and I/2, we have that
is the probability for the stick to be broken before the length a is reached following the stick from one starting point plus the probability for the stick to be broken after the length I-a from the same starting point. This means that
b) Note that, as a consecuence of what we calculate in the previous item, X has a uniform distribution with parameter I/2, therefore, the probability density function f is
f(x) = 1/(I/2) = 2/I
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So, how can we find the direct distance from his place of work to his home? We can use the Pythagorean Theorem (, where
and
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is the length of the hypotenuse). We know that the lengths of the legs are 10 and 2, which we can use in the formula, as shown below:
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The distance would be √104 miles, or approximately 10.2 miles.
Answer:
Neither of the two advertising options meet the goal.
Step-by-step explanation:
Every $4,000 spent on cable TV will reach 160 fans.
Therefore, the goal of reaching 200000 fans will be fulfilled by dollars i.e. $5 million which is greater than the budget of $3 million.
Now, every $2,750 spent on radio ads will reach 125 fans.
Therefore, the goal of reaching 200000 fans will be fulfilled by dollars i.e. $4.5 million which is again greater than the budget of $3 million.
Therefore, neither of the two advertising options meet the goal. (Answer)