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Let $X$ be the mean of a random sample of size 5 from a normal distribution with $\mu=0$ and $\sigma^{2}=125 .$ Determine $c$ so that $\operatorname{Pr}(\bar{X}<c)=$ $0.90$.

Let $X$ be the mean of a random sample of size 5 from a normal distribution with $\mu=0$ and $\sigma^{2}=125 .$ Determine $c$ so that $\operatorname{Pr}(\bar{X}<c)=$ $0.90$.

Introduction to Mathematical Statistics

Distributions of Functions of Random…

The Distributions of $X$ and $n S^{2} /…

A diskless client on a Class C Ethernet network uses DHCP. The DHCP server is on a Class B Ethernet network. Draw a figure of the networks with appropriate IP addresses for the client, server, and relay agent. Fill out a DHCP request and reply packet.

TCP/IP Protocol Suite

A diskless client on a Class C Ethernet network uses DHCP. The DHCP server is on a Class B Ethernet network. Draw a figure of the networks with appropriate IP addresses for the client, server, and relay agent. Fill out a DHCP request and reply packet.

TCP/IP Protocol Suite

Show an example of a DHCP packet with a padding option.

TCP/IP Protocol Suite

Questions asked

INSTANT ANSWER

1) A DNS client is looking for the names of the computer with IP address 132.1.17.8 and 128.3.5.17.5. Show both the query and response messages assuming that the names are mail.google.com and ict.mit.manipal.edu. Also, with response message include extra 1,536 bytes of authoritative data and send to the DNS client. Assume that DNS uses UDP service A) for communication. Refer the DNS packet format given in Fig. Q. 1 A Fig.Q.1A \begin{tabular}{|c|c|} \hline Identification & Flags \\ \hline Number of question records & \begin{tabular}{c} Number of answer records \\ (All Os in query message) \end{tabular} \\ \hline \begin{tabular}{c} Number of authoritative records \\ (All 0s in query message) \end{tabular} & \begin{tabular}{c} Number of additional records \\ (All Os in query message) \end{tabular} \\ \hline \end{tabular}

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Let \( X \) have a Poisson distribution with mean \( \theta \). Test the simple hypothesis \( H_{0}: \theta=0.5 \) against the composite hypothesis \( \theta<0.5 \) by using a sample \( \left(X_{1}, \ldots, X_{12}\right) \) of size 12. Reject \( H_{0} \) if and only if the observed value of \( Y= \) \( X_{1}+\cdots+X_{12} \leq 2 \). Find the powers \( K\left(\frac{1}{2}\right), K\left(\frac{1}{3}\right), K\left(\frac{1}{4}\right), K\left(\frac{1}{6}\right) \), and \( K\left(\frac{1}{12}\right) \). What is the significance level of the test?

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INSTANT ANSWER

Let \( Y \) have a binomial distribution with parameters \( n \) and \( p \). We reject \( H_{0}: p= \) \( \frac{1}{2} \) and accept \( H_{1}: p>\frac{1}{2} \) if \( Y \geq c \). Find \( n \) and \( c \) to give a power function \( K(p) \) which is such that \( K\left(\frac{1}{2}\right)^{2}=0.1 \) and \( K\left(\frac{2}{3}\right)=0.95 \), approximately.

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INSTANT ANSWER

Let \( X \sim U[0, \theta] \). Test \( H_{0}: \theta=1 \) against \( H_{1}: \theta=2 \) using a sample \( \left(X_{1}, X_{2}\right) \) of size 2, by rejecting \( H_{0} \) if either \( \bar{X}>0.75 \) or at least one of \( X_{1} \) and \( X_{2} \) is greater than 1 . Compute \( K(1) \) and \( K(2) \).

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ANSWERED

Ivan Kochetkov verified

Numerade educator

The table below lists the observed results of ( n=120 ) independent throws of a die. egin{tabular}{|r||c|c|c|c|c|c|} hline Face & 1 & 2 & 3 & 4 & 5 & 6 \ hline Frequency & ( a ) & 20 & 20 & 20 & 20 & ( 40-a ) \ hline end{tabular} For what values of ( a ) would the hypothesis that the die is unbiased be rejected at 0.025 level of significance in a chi-square test?

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ANSWERED

Ivan Kochetkov verified

Numerade educator

A manufacturer of lightbulbs claims that the lightbulbs produced fall into five categories A, B, C, D, and E by quality, from highest to lowest, and that the percentages of lightbulbs in these five categories are 15, 25, 35, 20, and 5 respectively. A contractor who purchases a large number of the lightbulbs tests the claim by taking a random sample of 30 lightbulbs and observes that the numbers of lightbulbs that fall in the categories A, B, C, D, and E are 3, 6, 9, 7, and 5 respectively. Test whether the manufacturer is speaking the truth, using a chi-square test (i) at 5% significance level; (ii) at 1% significance level.

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INSTANT ANSWER

Exercises Let \( X \) have a Poisson distribution with mean \( \theta \). Test the simple hypothesis \( H_{0}: \theta=0.5 \) against the composite hypothesis \( \theta<0.5 \) by using a sample \( \left(X_{1}, \ldots, X_{12}\right) \) of size 12. Reject \( H_{0} \) if and only if the observed value of \( Y= \) \( X_{1}+\cdots+X_{12} \leq 2 \). Find the powers \( K\left(\frac{1}{2}\right), K\left(\frac{1}{3}\right), K\left(\frac{1}{4}\right), K\left(\frac{1}{6}\right) \), and \( K\left(\frac{1}{12}\right) \). What is the significance level of the test? 2. Let \( Y \) have a binomial distribution with parameters \( n \) and \( p \). We reject \( H_{0}: p= \) \( \frac{1}{2} \) and accept \( H_{1}: p>\frac{1}{2} \) if \( Y \geq c \). Find \( n \) and \( c \) to give a power function \( K(p) \) which is such that \( K\left(\frac{1}{2}\right)=0.1 \) and \( K\left(\frac{2}{3}\right)=0.95 \), approximately. 3. Let \( X \sim U[0, \theta] \). Test \( H_{0}: \theta=\frac{1}{X} \) against \( H_{1}: \theta=2 \) using a sample \( \left(X_{1}, X_{2}\right) \) of size 2, by rejecting \( H_{0} \) if either \( \bar{X}>0.75 \) or at least one of \( X_{1} \) and \( X_{2} \) is greater than 1. Compute \( K(1) \) and \( K(2) \).

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INSTANT ANSWER

3. In a normal distribution, \( 31 \% \) of the observations are under 45 and \( 8 \% \) are over 64 . Find the mean and standard deviation. 4. In a normal distribution, \( 7 \% \) of the observations are under 35 and \( 89 \% \) are under 63. Find the mean and standard deviation. 5. Suppose that the life lengths of two electronic devices \( D_{1} \) and \( D_{2} \) (in hours) have distributions \( N(40,36) \) and \( N(45,9) \) respectively. If the device is to be used for a 48 hour period, which device is to be preferred? 6. Suppose that the scores of an examination are normally distributed with mean 76 and standard deviation 15 . The top \( 15 \% \) scores receive grade \( \mathrm{A} \) and the bottom \( 10 \% \) receive grade F. Find (a) the minimum score to receive an \( \mathrm{A} \) (b) the minimum score to pass. 7. Suppose that the heights of 800 students are normally distributed with mean \( 66^{\prime \prime} \) and standard deviation \( 5^{\prime \prime} \). Find the number of students with heights (a) between \( 65^{\prime \prime} \) and \( 70^{\prime \prime} \) (b) greater than or equal to \( 6^{\prime} \). 8. In a certain examination, the percentages of candidates passing and getting distinction were 45 and 9 respectively. Assuming that the marks are normally distributed, 1

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ANSWERED

Lucas Finney verified

Numerade educator

3. Let ( ar{X} ) be the mean of random sample of size ( mathrm{n} ) from ( N(mu, 10) ). Find ( mathrm{n} ) such that the probability is approximately 0.95 that the random interval ( left(ar{X}-frac{1}{2}, quad ar{X}+frac{1}{2} ight) ) includes ( mu ).

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ANSWERED

Mengchun Cai verified

Numerade educator

2. Let (X, Y) is a two-dimensional random variable with the pdf f(x, y)=left{egin{array}{ll}x+y & 0 leq x, y leq 1 \ 0 & ext { elsewhere }end{array} ight.. Find the pdf of Z=X-Y.

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