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a. A discrete random variable can be described by the Binomial distribution if it satisfies four conditions. Briefly
discuss each of these conditions.
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- Explain. 2. group of 5 friends each scheduled with second dose of a Covid vaccine for a day in July. If each of the 31 days in July was equally likely to be selected by each of the friends, what is the probability that at least two of the friends have their vaccine on the same day?Which of the following is a feature of a binomial experiment? A. Each trial has an unlimited number of outcomes. B. The probability of a success is twice the probability of a failure. C. There are an uncertain number of trials. D. The probability of a success is the same for each trial.1. For each random variable described below, give its distribution (which will be Binomial, Geometric, Hypergeometric, Pascal, or Poisson) and the parameters of that distribution. (a) You are working on a difficult homework assignment with 5 problems. Every minute, you have an idea for the problem you are working on, but it only has a 5% chance of working. If it doesn’t work, you keep working on that problem, and if it works, you move on to the next problem. The random variable W is the time (in minutes) that it takes you to finish the homework assignment. (b) A standard 52-card deck is split equally between two players. The random variable X is the number of aces received by the first player. (There are four aces in the deck.) Note: this is a key parameter when playing the “card game” “War”. (c) Every time you turn on the light, the light bulb has a 1% chance of burning out and you have to replace it. The random variable Y is the number of times you turn on the light before you have…
- Suppose a random variable, x, arises from a binomial experiment. If n=6,and p=0.30, find the following probability. P(x=1)a) Example 5.5, Let 0.6 = probability that a patient recovers from a spread disease. If 12 people are known to have this disease, what is the probability that: ruci a. at least 10 survive, b. from 3 to 8 survive, c. exactly 5 survive, d. find the mean and variance of the binomial random variable! please solve ASAP
- If you sum the probabilities of the possible values of a discrete random variable, the result always equals ______.prove that if random variables X and Y have same characteristic function, then have same distribution.Determine which of these statements is correct/incorrect and explain the reason why. a. X is a discrete random variable. Therefore, P(9 < X < 11) = P(X=9) + P(X=10) + P(X=11) b. The probability of flipping two coins will result in one head and one tail is 1/2 c. K and L are mutually exclusive events. P(K)=0.3 and P(L)=0.4. Hence, P(K∩L) = 0.12 d. There are mass points that have a probability of zero. That is, if x is a mass point, then it's possible that P(X=x) = zero.
- Part 1 of 6 Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The number of light bulbs that burn out in the next year in a room with 13 bulbs b. The hair color of adults in the United States c. The number of pigeons in a country d. The time it takes for a light bulb to burn out e. The number of free-throw attempts before the first shot is missed f. The number of people in a restaurant that has a capacity of 150 ..... a. Is the number of light bulbs that burn out in the next year in a room with 13 bulbs a discrete random variable, continuous random variable, or not a O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable.Which of the following is an example of a discrete random variable? The amount of time it takes for a worker to complete a complex task. The monthly electric bill for a local business. The number of people eating at a local cafeteria between noon and 2:00 p.m.Example 2.3.28 A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4, and the probability that it contains 3 defective articles is 0.6. The articles are drawn one-by-one at random, and without replacement and they are tested till all defectives are found. What is the probability that the testing procedure ends at the twelfth testing?
