![Part D. In a communication system each data packet consists of 4000 bits. Each bit may be received in error with probability p 0.1, due to noise. It is assumed that bit errors occur independently. Let us denote N as the number of errors in one data packet. 18. Determine EN] b. 100 ?. 400 d. 1000 e. 4000 19. Determine Var[N] a. 0.01 b. 360 c. 1000 d. 1600 e. 160,000 20. Use the central limit theorem to find the probability that there are more than 430 errors in a certain data packet. a. 0.000021 b. 0.00032 C. 0.0043 d. 0.054 e. 0.65 21. Use the central limit theorem to find the probability P[380 SN S 420] a. 0.999 b. 0.98 c. 0.89 d. 0.79 e. 0.72 22. Use the central limit theorem to find the probability P[N 401]. b. 0.00013 C. 0.00026 d. 0.0046 e. 0.02](http://img.homeworklib.com/questions/b86dc860-0155-11ec-a851-2df04d931fcf.png?x-oss-process=image/resize,w_560)
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Part D. In a communication system each data packet consists of 4000 bits. Each bit may...
3. A data packet containing 18 bits is sent over a noisy communication channel. The probability...
3. A data packet containing 18 bits is sent over a noisy communication channel. The probability that the k-th bit is received correctly at the destination is 1 - p, and, therefore, it is erased with probability p. Erasures are independent over time. (a) 1 pt What is the probability that exactly 7 bits are erased from this packet? (b) 1 pt What is the maximum value of p such that the probability that the packet is received correctly (i.e.,...
please need a detailed answer! Thank you very much 28. An order of 4000 parts is...
please need a detailed answer! Thank you very much
28. An order of 4000 parts is received. Let random variable X be a number of defective parts. X follows a binomial distribution with n 4000, p .005. Using the central limit theorem, [normal approximation) a) find the probabilities : P(18 <X <21), P (X > 21) b) find the probability that average number of defective parts in 36 randomly chosen parts exceeds 21. c) Why is it possible to apply...
Internet packets can be classified as video (V) or as generic data ( D). Based on a lot of observations taken by the Internet service provider, we have the following probability model: P[V] = 3/4, P[D...
Internet packets can be classified as
video (V) or as generic data ( D). Based
on a lot of observations taken by the Internet
service provider, we have the following
probability model: P[V] = 3/4, P[D] =
1/4. Data packets and video packets occur
independently of one another. The random
variable Kn is the number of video packets
in a collection of n packets.
a) What is E[K100], the expected number
of video packets in a set of 100 packets?...
Find the sampling error: u = -5, B = -2.5, n= 100 -7.5 -2.5 0.25 2.5...
Find the sampling error: u = -5, B = -2.5, n= 100 -7.5 -2.5 0.25 2.5 Find M, and o, the mean and standard deviation of the sampling distribution of x: H= 25, 0=5, n= 10. M =25, o,=0.5 M =25, o,=1.58 M=2.5, o,=0.5 My=7.91, o,=1.58 B) A) Assume that the random variable X is normally distributed with mean = 52 and standard deviation = 10. Let n = 25. Find P(x>50). -0 0.16 0.84 D) A) B) C) D)...
Problem (Modified from Problem 7-10 on page 248). Suppose that the random variable X has the cont...
Problem (Modified from Problem 7-10 on page 248). Suppose that the random variable X has the continuous uniform distribution f(R) 0, otherwise Suppose that a random sample of n-12 observations is selected from this distribution, and consider the sample mean X. Although the sample size n -12 is not big, we assume that the Central Limit Theorem is applicable. (a) What is the approximate probability distribution of Xt Find the mean and variance of this quantity Appendix Table III on...
The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bar
(b) Find a 90% confidence interval for the P/E population mean μ of all large U.S. companies. (Round your answers to one decimal place.)Lower and upper limit(c) Find a 99% confidence interval for the P/E population mean μ of all large U.S. companies. (Round your answers to one decimal place.) lower and upper (d) Bank One (now merged with J. P. Morgan) had a P/E of 12, AT&T Wireless had a P/E of 72, and Disney had a P/E of 24. Examine the confidence intervals...
The number of programming errors in HW assignments by computer science students is assumed to follow...
The number of programming errors in HW assignments by computer science students is assumed to follow a Poisson distribution with mean l (so that the density function is f(x) = lambda ^ x * (e ^ - lambda) / x! ). a) Recall that the mean and variance of a Poisson distribution are both equal to l. A professor examines the distribution of the number of programming errors for one of her assignments. There were 50 assignments turned in. Suppose...
(b) (c) and (d) please Problem(5) (a) (1 pt) Let Z~ Normal(0, 1). Recall the definition...
(b)
(c) and (d) please
Problem(5) (a) (1 pt) Let Z~ Normal(0, 1). Recall the definition of z-value, i.e., P(Z > zr) = r. Find the probability of P(-70/2 < 3 < 2a/2). (b) (4 points) Let X1, X2, ... , Xn be a random sample from some population with (un- known) mean u and (known) variance o?. Based on the Central Limit Theorem and part (a) above, show that the confidence intervals for the population mean y can be...
4. Wireless Communications: Background: Per recitation, a wireless communication signal traveling from a cellphone tower to...
4. Wireless Communications: Background: Per recitation, a wireless communication signal traveling from a cellphone tower to your phone bounces off numerous obstacles, causing multiple copies of the transmitted signal with different delays to arrive at your phone. These copies can add constructively or destructively, resulting in an effect called "multipath fading". The simplest (and perhaps most common) model for such is Rayleigh fading, which is a consequence of the (celebrated) Central Limit Theorem that we will learn later in the...
1) Drawt (b) The normal f. with -50, ơ-10 (d) The expogEntial Ad.f with parameter λ...
1) Drawt (b) The normal f. with -50, ơ-10 (d) The expogEntial Ad.f with parameter λ raphs ofthe p.d.f. of the following distributions S (a) The standard no mal p.d.f. Ing (c) The unifo f. over interval [10, 20] 2. 2) Illustrating the central limit theorem Let X be a random variable having the exponential distribution with A-2. Denote by X,, X,, Xj, a sequence of independent variables with the same distribution as X. Define the sample mean x by...
3. A data packet containing 18 bits is sent over a noisy communication channel. The probability that the k-th bit is received correctly at the destination is 1 - p, and, therefore, it is erased with probability p. Erasures are independent over time. (a) 1 pt What is the probability that exactly 7 bits are erased from this packet? (b) 1 pt What is the maximum value of p such that the probability that the packet is received correctly (i.e.,...
please need a detailed answer! Thank you very much
28. An order of 4000 parts is received. Let random variable X be a number of defective parts. X follows a binomial distribution with n 4000, p .005. Using the central limit theorem, [normal approximation) a) find the probabilities : P(18 <X <21), P (X > 21) b) find the probability that average number of defective parts in 36 randomly chosen parts exceeds 21. c) Why is it possible to apply...
Internet packets can be classified as
video (V) or as generic data ( D). Based
on a lot of observations taken by the Internet
service provider, we have the following
probability model: P[V] = 3/4, P[D] =
1/4. Data packets and video packets occur
independently of one another. The random
variable Kn is the number of video packets
in a collection of n packets.
a) What is E[K100], the expected number
of video packets in a set of 100 packets?...
Find the sampling error: u = -5, B = -2.5, n= 100 -7.5 -2.5 0.25 2.5 Find M, and o, the mean and standard deviation of the sampling distribution of x: H= 25, 0=5, n= 10. M =25, o,=0.5 M =25, o,=1.58 M=2.5, o,=0.5 My=7.91, o,=1.58 B) A) Assume that the random variable X is normally distributed with mean = 52 and standard deviation = 10. Let n = 25. Find P(x>50). -0 0.16 0.84 D) A) B) C) D)...
Problem (Modified from Problem 7-10 on page 248). Suppose that the random variable X has the continuous uniform distribution f(R) 0, otherwise Suppose that a random sample of n-12 observations is selected from this distribution, and consider the sample mean X. Although the sample size n -12 is not big, we assume that the Central Limit Theorem is applicable. (a) What is the approximate probability distribution of Xt Find the mean and variance of this quantity Appendix Table III on...
(b)
(c) and (d) please
Problem(5) (a) (1 pt) Let Z~ Normal(0, 1). Recall the definition of z-value, i.e., P(Z > zr) = r. Find the probability of P(-70/2 < 3 < 2a/2). (b) (4 points) Let X1, X2, ... , Xn be a random sample from some population with (un- known) mean u and (known) variance o?. Based on the Central Limit Theorem and part (a) above, show that the confidence intervals for the population mean y can be...
4. Wireless Communications: Background: Per recitation, a wireless communication signal traveling from a cellphone tower to your phone bounces off numerous obstacles, causing multiple copies of the transmitted signal with different delays to arrive at your phone. These copies can add constructively or destructively, resulting in an effect called "multipath fading". The simplest (and perhaps most common) model for such is Rayleigh fading, which is a consequence of the (celebrated) Central Limit Theorem that we will learn later in the...
1) Drawt (b) The normal f. with -50, ơ-10 (d) The expogEntial Ad.f with parameter λ raphs ofthe p.d.f. of the following distributions S (a) The standard no mal p.d.f. Ing (c) The unifo f. over interval [10, 20] 2. 2) Illustrating the central limit theorem Let X be a random variable having the exponential distribution with A-2. Denote by X,, X,, Xj, a sequence of independent variables with the same distribution as X. Define the sample mean x by...
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