Question

Let Y be the random variable with the time to hear an owl from your room's open window (in hours). Assume that the probability that you still need to wait to hear the owl after y hours is: f(y) = 0.47-0.5 +0.52e-0.25 Find the probability that you need to wait between 2 and 4 hours to hear the owl, compute and display the probability density function graph as well as a histogram by the minute. Compute and display in the graphics the mean variance, and quartiles of the waiting times. (1.3)​

Answer 1

Answer:

And {\displaystyle a>0\;}{\displaystyle a>0\;}handjob {\displaystyle t\in [0,2\pi )\;\,}{\displaystyle t\in [0,2\pi )\;\,} This is the parameter equation for a three dimensional helix with radius a and moving 2π b units in the z-direction in each circle .

Similarly, a torus with major radius R and minor radius r can be expressed simply by the following parameter equations:

'Torus' with r=2 i and r=1/2

{\displaystyle x=\cos(t)(R+r\cos(u))\;}{\displaystyle x=\cos(t)(R+r\cos(u))\;}

{\displaystyle y=\sin(t)(R+r\cos(u))\;}{\displaystyle y=\sin(t)(R+r\cos(u))\;}

{\displaystyle z=r\sin(u)\;,}{\displaystyle z=r\sin(u)\;,}

And {\displaystyle t\in [0,2\pi ),}{\displaystyle t\in [0,2\pi ),} {\displaystyle u\in [0,2\pi ).}{\displaystyle u\in [0,2\pi ).}

Explanation:

{\displaystyle y=b\,\sin t}

Where {\displaystyle 0\leq t<2\pi }{\displaystyle 0\leq t<2\pi } There are limits to the parameter.

three dimensional helix

There are some geometric curves which are very difficult to express in Cartesian coordinates but are very easily expressed in the form of parameterized equations:

{\displaystyle x=a\cos(t)}{\displaystyle x=a\cos(t)}