Answer :
Using the uniform distribution:
a) The height of the density function which is f(x) is [tex]\frac{1}{12}[/tex]
We know that for a uniform distribution we have two bounds, namely a and b. The probability or likelihood of finding a value of at lower than x is given by the following formula:
P (X < [tex]x[/tex]) = [tex]\frac{x-a}{b-a}[/tex]
Now where we have been mentioned that the two bounds are as follows:
a = - 5 (lower bound)
b = 7 (upper bound)
a) To find the height (h) of the density function we use the below given formula:
h = [tex]\frac{1}{b-a}[/tex]
Putting here the values of a and b we get the height as,
∴ h = [tex]\frac{1}{7-(-5)}[/tex]
⇒ h = [tex]\frac{1}{7+5}[/tex]
⇒ h = [tex]\frac{1}{12}[/tex]
Hence, the height of the density function f(x) is [tex]\frac{1}{12}[/tex]
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