The probability density function
The value of
Aussie Maths & Science Teachers: Save your time with SmarterEd
A continuous random variable
The value of
A teacher coaches their school's table tennis team.
The teacher has an adjustable ball machine that they use to help the players practise.
The speed, measured in metres per second, of the balls shot by the ball machine is a normally distributed random variable
The teacher sets the ball machine with a mean speed of 10 metres per second and standard deviation of 0.8 metres per second.
--- 3 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
The teacher adjusts the height setting for the ball machine. The machine now shoots balls high above the table tennis table.
Unfortunately, with the new height setting, 8% of balls do not land on the table.
Let
--- 2 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
The teacher can also adjust the spin setting on the ball machine.
The spin, measured in revolutions per second, is a continuous random variable
--- 1 WORK AREA LINES (style=lined) ---
a.
b.
c.
d.
e.
f. This content is no longer in the Study Design.
g. This content is no longer in the Study Design.
h. This content is no longer in the Study Design.
The time Jennifer spends on her homework each day varies, but she does some homework every day.
The continuous random variable
--- 0 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
Let
Let
--- 6 WORK AREA LINES (style=lined) ---
--- 3 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
The probability density function
Find the value of
If a random variable
then
The probability density function of a continuous random variable
--- 5 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
a.
b.