Please answer the following questions and show your work for each as well as ans
ID: 3360755 • Letter: P
Question
Please answer the following questions and show your work for each as well as answer them.
1. The number of letters, X, delivered to our home each day is uniformly distributed between 3 and 10. Find
(a) The probabilty mass function of X.
(b) Prob[X < 8].
(c)Prob[X>8].
(d) Prob[X<=X<=5]
2. Messages relayed over a communication channel have probability p of being received correctly. A message that is not received correctly is retransmitted until it is. what value should p have so that the probabilty of more than one retransmission is less than 0.05?
Explanation / Answer
a)
P(X) = 1/7 if 3 < X < 10
P(X) = 0 if x < 3 Or x > 10
b)
P(X <8) = 8-3/10-3 = 5/7
c)
P(X > 8) = 1- P(X <=8)
= 1 - P(X <9)
= 1 - 6/7
= 1/7
d)
P(X <=5) = P(X < 6)
= 5-3/10-3
= 2/7