35 POINTS WILL MARK BRAINLIEST
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Answer:
(a) The value of fₓ (9.5) is 0.125.
(b) The value of fₓ (10.5) is 0.50.
Step-by-step explanation:
Let <em>X</em> denote delivery time of the mail delivered by Alice and <em>Y</em> denote delivery time of the mail delivered by Bob.
It i provided that:
The probability that Alice delivers the mail is, <em>p</em> = 1/4.
The probability that Bob delivers the mail is, <em>q</em> = 3/4.
The probability density function of a Uniform distribution with parameters [<em>a</em>, <em>b</em>] is:
The probability density function of the delivery time of Alice is:
The probability density function of the delivery time of Bob is:
(a)
Compute the value of fₓ (9.5) as follows:
For delivery time 9.5, only Alice can do the delivery because Bob delivers the mail in the time interval 10 to 12.
The value of fₓ (9.5) is:
Thus, the value of fₓ (9.5) is 0.125.
(b)
Compute the value of fₓ (10.5) as follows:
For delivery time 10.5, both Alice and Bob can do the delivery because Alice's delivery time is in the interval 9 to 11 and that of Bob's is in the time interval 10 to 12.
The value of fₓ (10.5) is:
Thus, the value of fₓ (10.5) is 0.50.
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
In this case we have the following equation of the line:
Where:
By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will have an equation of the form:
Substitute the given pointto find "b":
Finally, the equation of the requested line is:
Answer: