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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.
Answer:
Her answer is not correct because the sum cannot be less than either addend.
The correct answer is
Step-by-step explanation:
Given:
The expression to add is given as:
Alaina got the answer as
Let us first try to add the fractions and arrive at the answer.
Taking LCD of 18 and 20, we get LCD = 180
Now, making denominators of each fraction equal to 180 and changing the numerators accordingly.
Therefore, the result of Alaina is not correct because she got an answer which is less than the fraction . But when we add two fractions, the result must be greater than either of the addend.
Therefore, her answer is not correct because the sum cannot be less than either addend.