Answer:
a)
b)
Explanation:
Previous concepts
The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".
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). It is a particular case of the gamma distribution".
Part a
Let X the random variable of interest. We know on this case that
And we know the probability denisty function for x given by:
In order to find the cdf we need to do the following integral:
Part b
Assuming that , then the density function is given by:
And for this case we want this probability:
And evaluating the integral we got:
Maximum shear stress in the pole is 0.
<u>Explanation:</u>
Given-
Outer diameter = 127 mm
Outer radius, = 127/2 = 63.5 mm
Inner diameter = 115 mm
Inner radius, = 115/2 = 57.5 mm
Force, q = 0
Maximum shear stress, τmax = ?
τmax
If force, q is 0 then τmax is also equal to 0.
Therefore, maximum shear stress in the pole is 0.
Answer:
The pipe is open ended and the length of pipe is 3.4 m.
Explanation:
For identification of the type of pipe checking the successive frequencies in both the open pipe and closed pipe as below
Equation for nth frequency for open end pipe is given as
For (n+1)th value the frequency is
Taking a ratio of both equation and solving for n such that the value of n is a whole number
So n is a whole number this means that the pipe is open ended.
For confirmation the nth frequency for a closed ended pipe is given as
For (n+1)th value the frequency is
Taking a ratio of both equation and solving for n such that the value of n is a whole number
As n is not a whole number so this is further confirmed that the pipe is open ended.
Now from the equation of, with n=6, v=340 m/s and f=300 Hz
The value of length is 3.4m.