Please show all work! 1. Ten percent of items from a certain production line are

Question

Please show all work!

1. Ten percent of items from a certain production line are defective. What is the probability that there is more than one defective item in a batch of 100 items? 2. A block of 100 bits is transmitted over a binary communication channel with probability of bit error p = 10^-3. Find the probability that the block contains 4 or more errors. 3. A coin is tossed 4 times. Let the random variable Y be the difference between the number of heads and the number of tails. (a) Describe the sample space of Y, Sy.. (b) Find the equivalent event for the event {Y = 0}. (c) Is this a discrete or continuous random variable? (d) Find and plot the cdf for the random variable assuming that a fair coin is tossed.

Explanation / Answer

1.)

P(defective item <= 1) = P(0) + P(1) = 0.9100 + 100*0.1*0.999

P(defective item > 1) = 1 - P(defective item <= 1) = 1- 0.9100 - 100*0.1*0.999 = 0.9997

2.)

P(errors<4) = P(0)+P(1)+P(2)+P(3)

= 0.999100 + 100*0.001*0.99999 + 4950*0.0012*0.99998 + 161700*0.0013*0.99997

P(4 or more errors) = 1- P(errors<4) = 0.000136

3.)

a.)

SY = {-4,-2,0,2,4}

b.)

{Y=0} = {HHTT , HTHT , THTH , HTTH , THHT, TTHH }

c.)

Y is a Discrete random variable since it takes discrete values {-4,-2,0,2,4} with some discrete probability

d.)

P(Y = -4) = (1/2)4

P(Y = -2) = 4(1/2)4

P(Y = 0) = 6(1/2)4

P(Y = 2) = 4(1/2)4

P(Y = 4) = (1/2)4

F(Y) = 1 for Y>=4

F(2)= F(3)=15/16

F(0)= F(1)= 11/16 for Y=0,1

F(-2)= F(-1)= 5/16 for Y= -2,-1

F(-4)= F(-3)= 1/16 for Y= -4,-3

F(Y)= 0 for Y<= -5

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.