There are 1800 gym members in total. 3 4 are aged 25 - 59 years, 1 5 are over 60 years and the remainder are under 25 years. How
1 answer:
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Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
Answer:
c) 761.0
Step-by-step explanation:
Previous concepts
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
The random variable is given by this table
X | 0 | 10 | 50 | 100 |
P(X) | 1/40 | 1/20 | 1/10 | 33/40 |
In order to calculate the expected value we can use the following formula:
And if we use the values obtained we got:
In order to find the variance, we need to find first the second moment, given by :
And using the formula we got:
Then we can find the variance with the following formula:
And then the standard deviation would be given by:
So then the best answer for this case is:
c) 761.0