On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she does so at a time that is uniformly distributed between 9 and 11 . If Bob delivers it, which happens with probability 3/4 , he does so at a time that is uniformly distributed between 10 and 12 . The PDF of the time X that mail gets delivered satisfies a) fX(9.5)= unanswered b) fX(10.5)=

(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 X denote delivery time of the mail delivered by Alice and Y denote delivery time of the mail delivered by Bob.

It i provided that:

The probability that Alice delivers the mail is, p = 1/4.

The probability that Bob delivers the mail is, q = 3/4.

The probability density function of a Uniform distribution with parameters [a, b] 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.

t= half of the arc subtended by t.

r= half of the arc subtended by r.  

t+r= half of the arc subtended by t + half of the arc subtended by r= half of 360=180

step-by-step explanation: