We toss n coins, and each one shows heads with probability p, independently of each of the others. Each coin which shows heads is tossed again. What is the mass function of the number of heads resulting from the second round of tosses?
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- Calculate each Poisson probability: a. P(X= 6), A =7 (Round your answer to 4 declmal places.) Probability b. P(X= 11), A = 10 (Round your answer to 4 declmal places.) Probability c. P(X= 2). A = 9 (Round your answer to 4 declmal places.) ProbabilitySolve it soonLet X = daily number of bag of rice a farmer harvest. The farmer modeled X and got the following probability mass function. X 0 1 2 3 4 P(X=x) 0.1 0.4 0.25 0.15 0.10 a. The probability that the farmer will harvest 5 bags of rice today is? b. The probability that the farmer will harvest at least 2 bags of rice today? c. The amount of bags of rice the farmer harvest for a day on the average is? d. If the farmer gets $300 per bag, what is the farmer's average daily earnings? e. What is the variance of X?
- Solve it soonShow work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?2. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.
- This is part B of the question! In a certain population we nd that 60% of people have brown eyes. For these exercises, we will select 10 people at random from this population. Let X denote the number of people having brown eyes in the group. Part A: 1. Find the probability mass function of X.2. Find the cumulative distribution of X.3. What is the probability that there are at most 3 people with brown eyes in the sample? Part B: 4. the expected number of people with brown in the sample?5. Find the standard deviation of the number of people with brown eyes in thesample.Two coins are taken at random (without replacement) from a bag containing 6 nickels, 5 dimes, and 4 quarters. Let X denote the random variable given by the total value of the two coins. Find E(X). (Round your answer to four decimal places.)Two on and off valves are in parallel and act independently. They control the fluid that flows through the pipe. Suppose that valve A has a 60% chance of being off and a 40% chance of being on. Valve B has a 40% chance of being off and a 60% chance of being on. A Determine the probability that fluid flows through the pipe. Choices: 1, 0.76, 0.64, 0.36, 0.24, 0.16 Determine the probability that flue will not flow through the pipe. Choices: 1, 0.76, 0.64, 0.36, 0.24, 0.16
- Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x