The probability of a bit error in a memoryless binary symmetric communication channel is 10^-3. Find the probability of a block of 1000 bits has five or more errors.
A student needs 12 chips of a certain type to build a circuit. It is known that 5% of these chips are defective. At least how many chips should she/he buy for there to be a greater than 95% probability of having enough chips for the circuit?
3. Let {N(t)}>0 be a renewal process for which the interarrival times {T1,T2,. . .} have cumulative distribution function F. Recall that the renewal function m(t) is given by m(t) E[N(t)j. (a) Find E[N(t)Ti=x] fort<x andfortx. (b) Find E[N(t)] E[E[N(t) T1]] to prove that m(t) satisfies the renewal equation m(t) F(t) + f m(t
1. Suppose that shocks occur according to a Poisson process with rate A> 0. Also suppose that each shock independently causes the system to fail with probability 0 < p < 1. Let N denote the number of shocks that it takes for the system to fail and let T denote the time of the failure. (a) FindP{T>tNrrn}. (b) FindP{NrrnT=t}. (
A box contains 3n red balls and 3n white balls. 2n balls are selected at random without replacement, express the probability p that the balls selected contain n red and n white. Use Stirling's formula to obtain the approximation p ~ root(3/(2*pi*n))
Suppose the probabilities that a new car battery functions For at least 20, 000km is 0.8 For at least 40, 000km is 0.5, For at least 60, 000km is 0.1. (i) Given that the battery still works at 20, 000 km, what is the probability that it lasts for at least another 20, 000km? (ii) Given that the battery still works at 20
Two friends Dave and Pete often play squash and tennis together. Over the years, they have found that Dave wins 3 out of every 5 rounds of squash and 1 out of every 4 tennis matches. If they play one match of squash and then one tennis match: a) Draw a tree diagram to describe the situation b) Find the probability that Dave
1. Each of the three measures of central tendency-the mean, the median, and the mode-are more appropriate for certain populations than others. For each type of measure, give two additional examples of populations where it would be the most appropriate indication of central tendency. 2. Find the mean, median, and mode of
I cannot find the famous distribution that describes the frequency of the number of times a number comes up in a series of dice rolls? I think the answer is the distribution was discovered by Siméon-Denis Poisson (1781-1840). In probability theory and statistics, the Poisson distribution is a discrete probability distribut
1. True or False? The standard deviation of a population will always be smaller than the standard deviation of the sample means (of the samples used to estimate this same population). 2. The mean height for a population is 65 inches and the standard deviation is 3 inches. Let X_ denote the mean height for a sample of people
The Powerball For a single ticket, a player first selects five numbers from the numbers 1-53 and then chooses a powerball number, which can be any number between 1 and 42. A ticket costs $ 1. In the drawing, five white balls are drawn randomly from 53 white balls numbered 1-53, and one red Powerball is drawn randomly from
See the attached files. Recall that the case study in your text concerns an amazing event that occurred during the second round of the 1989 US Open at Oak Hill in Pittsford, New York. Four golfers--Doug Weaver, Mark Wiebe, Jerry Pate, and Nick Price--made holes-in-one on the sixth hole. Recall from your text that the probabi
The sign "I LOVE MATHEMATICS" is put on the wall of the mathematics building at South Central Carolina Technical College. The letters start to fall off of the sign. Find the probability of each of the following events. 1.. The first letter that falls off is "M" . 2. The second letter that falls off is an "A" knowing tha
1. A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a: a. payback period matrix. b. decision matrix. c. decision tree. d. payoff table. 2. The difference between expected payoff under certainty and expected value of the best act without certainty is
1. Event A: You spend your entire Memorial Day 2006 in Acapulco. Event B: You spend your entire Memorial Day 2006 with some of your friends. TRUE OR FALSE: A and B are mutually exclusive events. 2.Event A: You spend your entire Memorial Day 2004 in Denver. Event B: You spend your entire Memorial Day 2004 in Vermont. TRU
1. A coin is tossed 3 times. Discrete random variable X is equal to the number of times Heads comes up. Discrete random variable Y has the value 1 if the first toss comes up heads and 0 otherwise. (a) Find Pr[(X=1)n(y=1)] Are X and Y independent random variables?
7. There are some tokens in a bag. Each token has a number ( a positive integer) printed on it. Ernesto does not know how many tokens are in the bag, and the only thing he knows about the numbers on them is that the mean of the numbers is 3 and the variance is 2. Ernesto is going to play a game in which he draws 1 token from th
5. Let E be the event that the number which comes up when a single die is tossed is divisible by 3. Let X be the number of times that event E occurs in 3 tosses of the die. (a) Make a table showing the pdf and the cdf of X. (b) Find E(X) and V(X).
4. A hand of 5 cards contains 2 red cards and 3 black cards. Trish plays the following game: A card is drawn from the hand. If the card is red, the game stops immediately. If the card is black, this black card is set aside and a red card is put into the hand in its place. Then another card is drawn from the hand and the same pro
3. There are 13 standard decks of cards. Each deck is shuffled, separately. The 13 decks are lined up in a row on the table. The top card is drawn from each deck. What is the probability that at least 3 cards of each suit are drawn?
1. There are 3 boxes. Each box contains several envelopes. Some envelopes have "you lose" written on them. The rest say "you win..." . However, of the ones that say "you win..." , some contain only a piece of paper saying "... nothing" . Each of the other contains a $5 bill. The first box contains 3 "lose" envelopes and 2 so-
Problem 4. Let X denote the number of boys in a family with four children. Pr(X > 3) is? a. 5/16 b. ¼ c. 11/16 d. 2/3 e. None of the above
Problem: The APR for a 30 year, $250,000 mortgage at 6% interest compounded monthly and two discount points is: A. 6.25% b. 6.19% c. 6.12% d. 5.87% e. None of the above.
Suppose that a probability distribution has a mean 20 and standard deviation 3. The Chebychev inequality states that the probability that an outcome lies between 16 and 24 is: a. less than 7/16 b. at least 7/16 c. at most 1/4 d. at least 1/4 e. none of the above
Two people play a game. A single die is thrown. If the outcome is a 2 or a 3, then player A pays player B $6.00. How much should B pay A when a 1, 4, 5, or 6 is thrown so that A and B break even, on average, over many repititions of the game? a. $2.00 b. $8.00 c. $4.00 d. $6.00 e. None of the above
The test scores of 30 students are listed Below. Find Q3; 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99
1. s1 s2 s3 d1 10 8 6 d2 14 15 2 d3 7 8 9 What decision should be made by the conservative decision a. D1 b D2 c. D3 2. s1 s2 s3 d1 10 8 6 d2 14 15 2 d3 7 8 9 If the probabilities of s1, s2, and s3 are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the e
How many poker hands consist of four clubs and a card of a different suit? a. 48 * C(13,4) b. 39 * C(52,4) c. 48 * C(52,4) d. 39 * C(13,4).
A light Bulb manufacturer tests a light bulb by letting it burn until it burns out. The experiment consists of observing how long (in hours) the light bulb burns. Let E be the event "the bulb lasts less than 100 hours", F be the event "the bulb lasts less than 50 hours",and G be the event "the bulb lasts more than 120 hours." T
P(8,5) = a. 5!/8! b. 8*7*6*5*4 c. 8*7*6*5 d. 8!/5!3!