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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: False
Step-by-step explanation:
We know that , If p-value < , we reject the null hypothesis .
If p-value ≥ , we are fail to reject the null hypothesis .
As per given , we have
The p value for an independent samples t-test is 0.043.
The level of significance is
Since , 0.043 < 0.05.
i.e. p-value <
It means we reject the null hypothesis .
It means the null hypothesis is false.
Hence , the correct decision in this scenario is to favor the null hypothesis : False